arXiv:1810.06412v1 [physics.hist-ph] 5 Oct 2018 pnAcs.©21 .Porceddu S. 2018 © Access. Open oeiaie . License 4.0 NoDerivatives 1 Finland Helsinki, of sity ae noAcetEyta agaei h ito Appendix of list the in language Egyptian Ancient into lated ötne,Germany Göttingen, Finland Finland esni Finland Helsinki, land fPyis nvriyo esni Finland; sebastian.porceddu@helsinki.fi Helsinki, Email: of University Physics, of Abstract: 2018 04, May accepted 2018; 15, Feb Received https://doi.org/10.1515/astro-2018-0033 the of motives the observations the Calendar: and Cairo means the possible in Horus as Algol Toivari-Viitala Jaana Joonas and Markkanen, Lehtinen, Tapio Jetsu, Lauri Porceddu*, Sebastian Article Research 232–264 27: 2018; Astron. Open satvt fgd eelwyAglrcie h il fHor of title the received Keywords: Algol why reveal gods observ of Here astronomical mille activity how. such as three for especially motives Algol and the and CC binary means into eclipsing possible period the Algol’s of recorded who period astrophys astronomical, the Previous was days. this 2.850 of period the a,o ato h a,i osdrd“good” considered is day, the the al. of whether part et denote a or (Helck day, prognoses and These p127-147) (Bacs p156). 1975–1992, 1989, p1-2) (Troy 1994, p41-45) (Leitz Egyptian 1990, p117-118), the of 2001a, day (Wells literary each year to are prognoses hemerologies, of assign or that Calendars works Days, the Unlucky as and known Lucky texts Egyptian ancient The Introduction 1 esuytebs rsre n fteenn et,CC, texts, nine these of one Here, preserved p328). best 2008, the al. study et we (Porceddu and p-2) 1994, (Leitz 1 an Toivari-Viitala: Jaana yiLehtinen: Jyri etuKajatkari: Perttu onsLyytinen: Joonas ai Markkanen: Tapio ar Jetsu: Lauri orsodn uhr eata Porceddu: Sebastian Author: Corresponding iesc et aebe on To 99 p140-143), 1989, (Troy found been have texts such Nine euetesmo “ symbol the use We nacetEyta aedro uk n nuk as h C the Days, Unlucky and Lucky of Calendar Egyptian ancient An lo,Hrs nin gpinAtooy aibestars, variable Astronomy, Egyptian ancient Horus, Algol, eateto hsc,Uiest fHlik,Fin- Helsinki, of University Physics, of Department a-lnkIsiu ü Sonnensystemforschung, für Max-Planck-Institut eateto hsc,Uiest fHelsinki, of University Physics, of Department eateto hsc,Uiest fHelsinki, of University Physics, of Department N odnt h od n hae trans- phrases and words the denote to ” eateto hsc,Uiest of University Physics, of Department eateto ol utrs Univer- Cultures, World of Department tal. et ulse yD rye.Ti oki iesdudrteCetv Commons Creative the under licensed is work This Gruyter. De by published , N r“bad” or Department A. N . cladsaitclaaye fC upr h dathat idea the support CC of analyses statistical and ical sbihe hnAglB oee,AglBhsalarger a has B A Algol Algol However, days. B. 2.867 Algol of than period com- brighter a a is around with orbit mass B, of binaries. Algol centre eclipsing and mon called A stars Algol of stars, two class The a ( of prototype Algol a of is the period to seemingly days close one rather 2.867 was current that days, noted a 2.850 In was period, significant p334). it less 2008, study, al. that et of (Porceddu footnote periods well other as few test, Rayleigh a the as called method statistical a with (1994, Leitz and hi- English) German). the in in the by (1966, from Bakir assisted us of (1994), by translations Leitz translated of been transcription have eroglyphic article quote we this passages text in CC noise All random analysis. the a to introduce component would Calendar from Cairo any created long dataset combining the the so to sources we describe, these from and they points year apparent data what not know is not calendar these do main of the connection the to because fragments analysis ig- this other are from papyrus The same nored 86637. the in Cairo contained papyrus fragments and of texts I-IX verso and 2013; XXX al. et calendar Jetsu use continuous we pre- 2008; 2015), three Porceddu al. and our et Jetsu all (Porceddu in As studies Bakir. vious pub- el-Mohsen and Abd p156), by 1975–1992, al. lished et (Helck and Walsem (Van p233) p2-5), 1982, 1966, (Bakir B.C. 1271-1163 to dated tos hi rnilso eciigclsilphenomen celestial describing of principles Their ations. us naao oee,nx ontigi nw about known is nothing to next However, ago. nnia eso htteacetEyta cie a the had scribes Egyptian ancient the that show we , h yoi eido h onwsdsoee nCC in discovered was Moon the of period synodic The h ar aedr hemerologies Calendar, Cairo the ytnn etuKjtai Jyri Kajatkari, Perttu Lyytinen, ioClna C) sin ukwith luck assigns (CC), Calendar airo hc sfudo ae et III- recto pages on found is which Attribution-NonCommercial- nytebs preserved best the only β esi.Ti star This Persei). a S. Porceddu et al., Algol as Horus in the Cairo Calendar 233 radius than Algol A. Our line of sight nearly coincides (1783) determined the 2.867 days period of Algol in 1783. with the orbital plane of this double star system. There- A close friend and tutor of John Goodricke, Edward Pig- fore, these stars eclipse each other during every orbital ott, also discovered several new variable stars (Hoskin round. In a primary eclipse, the dimmer Algol B partly 1979). In his last paper, Pigott (1805, p152) argued that eclipses the brighter Algol A. This primary eclipse can the brightness of Algol must have been constant in An- be observed with naked eye. In a secondary eclipse, the tiquity, because the variability that he observed was so brighter Algol A partly eclipses the dimmer Algol B, but easy to notice with naked eyes. Kopal (1946, p3) sug- the decrease in total brightness of this binary system is gested that those ancient discoveries “may have been so small that this secondary eclipse event can not be ob- buried in the ashes of the Library of Alexandria”. More re- served with naked eye. Hence, the brightness of Algol ap- cently, Wilk (2000) has presented the theory that classical pears to remain constant for a naked eye observer, except mythology contains knowledge of the variability of vari- during the primary eclipses. These primary eclipses last ous stars, including Algol. This star also seems to belong about ten hours. For most of the time, Algol is brighter to the constellation called “Elk” by the Siberian shamans than its six close-by bright comparison stars (Jetsu et al. of the Khanty tribe, who have noticed that this animal 2013, their Figure 5a). During a primary eclipse, Algol sometimes loses one pair of legs (Pentikäinen 1997, p58- first becomes dimmer for five hours and then regains its 65). brightness in another five hours. For a few hours, Algol A statistical analysis of 28 selected words (hereafter appears visibly dimmer than all its six comparison stars. SWs) of the mythological narratives of CC was performed A naked eye observer can easily notice this as a clear to find traces of the Egyptians’ symbolism for Algol (Jetsu change in Algol’s constellation pattern. and Porceddu 2015). We notate the SWs of that par- The normalized Rayleigh test of the CC data con- ticular study for example “Horus” or “Seth” to distin- firmed the high significance of the 2.850 days period guish them from other Egyptian deities such as Isis and (Jetsu et al. 2013). The period increase from 2.850 to Nephthys. Out of all 28 SWs, the word “Horus” had the 2.867 days during the past three millennia gave a mass strongest connection to the 2.850 days periodicity (Jetsu transfer rate estimate from Algol B to Algol A. This esti- and Porceddu 2015). “Horus”, etymologically “the distant mate of Jetsu et al. (2013) agreed with the one predicted one”, was one of the earliest attested Egyptian deities. by the best evolutionary model of Algol (Sarna 1993, Predominantly a sky god or stellar god, the living king p540). A sequence of eight astronomical criteria was also was identified as an earthly “Horus” (Roeder 1994, p42- presented which proved that the ancient Egyptians could 43) and (Meltzer 2001, p119-122). Horus is described as a have discovered Algol’s periodic variability with naked star in the oldest ancient Egyptian texts (Krauss 2016). eyes (Jetsu et al. 2013, p9-10), i.e. it is the star where it Another deity, “Seth”, the adversary of “Horus”, was is easiest to discover regular short-term variability with- shown to be connected to the period of the Moon (Jetsu out the aid of a telescope. and Porceddu 2015). In the Hellenistic tradition, Algol was called “the Statistical analyses have confirmed the ancient Egyp- head of Gorgon”. Similar tradition was continued in the tian discovery of Algol’s period (Porceddu et al. 2008; Arabic name “Demon’s Head”. The name Algol is derived Jetsu et al. 2013; Jetsu and Porceddu 2015). Here, our from the Arabic word, head of the Ghoul (ra’s al-gh¯ul) aim is to connect this astonishing ancient discovery to its (Davis 1957). These names seem to indicate that some contemporary cultural and historical background by pre- exotic or foreboding feature or mutability was known in senting ten general arguments about CC (Sects 4.1-4.10). the folklore of the ancient peoples. All the way to me- These arguments strongly support the idea that the an- dieval astrology, the ill omens associated with the “evil cient Egyptian scribes had the possible means and the eye” of Algol were known, so it is actually surprising that motives to record Algol’s period into CC. The connection it is so difficult to find any direct reference to Algol’s vari- of CC mythological texts to the perceived behaviour of ability in old astronomical texts (Davis 1957). The list of the Moon and Algol is verified in Sects 4.7 and 4.8. ill-omened names is so impressive (Allen 1899, p332-333) that it is unlikely that the variability would have gone undetected through millennia of practical star observing by the ancient Egyptians. Of the modern astronomers, Fabricius discovered the first variable star, Mira, in 1596. The second variable star, Algol, was discovered by Montanari in 1669. Goodricke 234 S. Porceddu et al., Algol as Horus in the Cairo Calendar

2 2 Materials and Methods 1) . For example, the GGG prognosis combination for the date I Akhet 27 means that all the three parts of the day are lucky. This fully positive prognosis is the most 2.1 Materials common for any day. Kemp and Rose (1991) noted that the ratio of good and bad prognoses in CC is close to the We use statistical methods to discover the principles value of the so-called Golden Section, in accordance with of describing celestial phenomena in CC, thus no other modern psychological experiments regarding positive and Egyptian texts are used as material in the core analysis. negative judgements. We begin with a general description of CC. Generally speaking, on SSS days people were under This document is one of the texts known as Calendars a special threat to suffer from hunger, thirst and various of Lucky and Unlucky Days. In these Calendars the days illnesses. The prognoses of such days were attributed to of the year are assigned good and bad prognoses. Nine full mostly negative mythological events and children born on and partial Calendars of Lucky and Unlucky Days have such a date might have been foretold to die of illness. On been discovered (Leitz 1994, p1-2), (Troy 1989, p140-143) the other hand, those born on GGG days would live a long and (Helck et al. 1975–1992, p156). Eight of them date to life. Such days were in general supposed to consist of joy, the New Kingdom, ca. 1550-1069 B.C., while one of them success, freedom, health and various feasts. While on SSS is from the Middle Kingdom, ca. 2030-1640 B.C. Papyrus days some restrictions were suggested on journeying and Cairo 86637, the source of CC, was originally dated to consumption of foods, on GGG days it was recommended the ninth regnal year of Ramses II (Brunner-Traut 1970), to give offerings and feasts to the gods (Troy 1989, p138). around 1271-1270 B.C. according to the generally ac- In the longer and better preserved texts, especially in cepted chronology (Shaw 2000, p480-490) which has been CC, there are descriptions of mythological events relating disputed (Huber 2011). However, the date is nowhere to to the date and also some instructions on suggested be- be explicitly found (Leitz 1994, p1-2). Van Walsem (1982, haviour during the day (FAQ 1). For example, regarding p233) revised the date of the papyrus to the early 20th the day I Akhet 27 the description in CC, page recto VIII, dynasty, around 1185-1176 B.C. We have also checked reads that the god “Horus” and his enemy “Seth” are rest- the paleographical correspondences of plentifully recur- ing from their perpetual struggle. It is recommended not ring signs, such as F35, G17, N5, O1 and R8 (Wimmer to kill any “snakes”Nduring the day. The practical influ- 1995, p118,129,194,246,274), and these seem to support ence of the Calendars of Lucky and Unlucky Days on the the conclusion of dating the manuscript to the latter half life of ancient Egyptians is not exactly known. The var- of the 19th dynasty or the beginning of the 20th, i.e. ious instructions and restrictions such as “make offering 1244-1163 B.C. A compromise date 1224 B.C. was used in to the gods of your city” (Leitz 1994, p82) or “do not go the astrophysical and astronomical computations (Jetsu out of your house to any road on this day” (Leitz 1994, et al. 2013, p1), as well as in the SW analysis (Jetsu and p238) seem to be presented in the context of the everyday Porceddu 2015, p1). The results of both of those studies life of a worker. It was suggested that the Calendars of did not depend on the exact dating of CC. Lucky and Unlucky Days would have determined the rest CC is a calendar for the entire year. We use the days for the workers (Helck et al. 1975–1992, p153-155), daily prognoses of CC published in Table 1 of Jetsu et al. but no correlation of the Lucky and Unlucky Days was (2013), where the German notations by Leitz (1994, p480- found with days of kings’ ascensions to throne, official 482) were used (G=Gut= “good”, S=Schlecht=“bad”). building works, battles, journeys, court trials or working CC is based on the Civil Calendar of 12 months of 30 days, except when the day was also a regular feast date days each plus five additional epagomenal days for which (Drenkhahn 1972, p87-94). In CC, the prognosis of the no prognoses are given. The months were arranged into first day of each month is always GGG and the day is three seasons of four months each. These seasons were called “feast”N. On the other hand, the prognosis of the Akhet (flood season)N, Peret (winter season)Nand Shemu N 20th day of each month is always SSS. (harvest season) . The conventionally given format for a In most cases, the prognosis is homogeneous for the calendar date is for example I Akhet 27 for the 27th day whole day (i.e. GGG or SSS). There are only 29 heteroge- of the first month of the Akhet season. The CC texts systematically give a date, inscribed in red colour, and then three prognoses for that date (FAQ 2 Some frequently asked questions (FAQ) about our research have been collected into Appendix B, where we give short an- swers those questions, as well as indicate the sections of this manuscript where the more detailed answers can be found. S. Porceddu et al., Algol as Horus in the Cairo Calendar 235 neous prognoses in CC. These days provide a glimpse into Table 1. “GGG” prognosis texts mentioning Horus, the logic behind the day division. Generally speaking, ar- Wedjat or Sakhmet. The columns are SW (Selected word), ancient Egyptian month (“Month”), day (D), numerical month rangement into morning, mid-day and evening is obvious, value (M), time point (g(D,M)) and the phase angles (ΘAlgol but these can be defined in multiple ways. For example, and ΘMoon). All values are in the order of increasing ΘAlgol, the prognosis for the date I Akhet 8 in CC is GGS. The because this allows an easy comparison with the results shown in text advises one not to go out during the “night”N. The List 1 and Figure 1. prognosis for I Akhet 25 is also GGS but the text advises N one not to go out during the “evening” . Thus it remains SW Month D M g(D,M) ΘAlgol ΘMoon unclear if the third part of the day comprises night hours Horus II Akhet 14 2 43.33 6 124 Wedjat I Peret 1 5 120.33 13 341 as well. Jetsu et al. (2013, p2-7) showed that the period Sakhmet I Peret 1 5 120.33 13 341 analysis results for CC did not depend on how the three Horus IV 19 12 348.33 13 234 prognoses were distributed within each day. Shemu The practice of assigning good and bad omens to Horus I Akhet 27 1 26.33 19 278 days of the year seems rather close to astrology and read- Horus III Akhet 24 3 83.33 19 251 Horus III Peret 1 7 180.33 32 351 ing predictions from the stars, and indeed the Calendar Horus III Akhet 27 3 86.33 38 287 of Lucky and Unlucky Days was mixed with Babylonian Horus III 15 11 314.33 38 180 based astrology in the Greek and Roman times (Leitz and Shemu Thissen 1995, p38-55). But it is to be noted that celestial Horus I Shemu 1 9 240.33 51 0 matters did not fully determine the prognoses in the Cal- Wedjat II Akhet 3 2 32.33 57 351 endar of Lucky and Unlucky days, but played a part in Horus I Shemu 7 9 246.33 88 73 Horus III Akhet 28 3 87.33 164 300 it alongside natural cycles such as the floods of the Nile, Horus II Shemu 1 10 270.33 240 5 or the seasonal dangers presented by winds, wild animals Sakhmet IV Akhet 16 4 105.33 278 158 and illnesses. There is also plenty of evidence for various Horus III Peret 23 7 202.33 291 258 kinds of ritual recurrence, such as that III Akhet 26 is Horus III Akhet 29 3 88.33 291 312 described the strengthening of “the djed-pillar”N (Helck Sakhmet I Peret 9 5 128.33 303 78 Wedjat II Shemu 30 10 299.33 303 358 et al. 1975–1992,a ritual object whose raising is connected Sakhmet I Peret 29 5 148.33 309 321 to the myth of the resurrection of the god Osiris who was Horus I Akhet 18 1 17.33 322 168 killed by Seth) and II Peret 6 is described the erection Wedjat I Shemu 6 9 245.33 322 61 of “the djed-pillar”, with a separation of exactly 70 days, the approximate interval between Sirius’ heliacal setting Table 2. “SSS” prognosis texts mentioning Horus, and Sirius’ heliacal rising. It was considered the ideal du- Wedjat or Sakhmet. Notations are as in Table 1. ration of funerary ceremonies because the star was be- lieved to spend this time in the underworld, undergoing SW Month D M s(D,M) ΘAlgol ΘMoon rituals of purification. CC also makes explicit references Horus IV Peret 5 8 214.33 6 44 to the heliacal rising, culmination and heliacal setting of Horus I Akhet 26 1 25.33 253 265 Horus III 11 11 310.33 253 132 certain hour-stars (Hardy 2003). All prognoses based on Shemu this type of aperiodic events induce statistical noise into Wedjat II Peret 10 6 159.33 259 95 CC. When applying period analysis to the CC data, this Sakhmet IV Peret 27 8 236.33 265 312 noise interferes with the detection of any periodic signal. Sakhmet II Peret 13 6 162.33 278 132 When searching for regular periodic astronomical Sakhmet II Shemu 7 10 276.33 278 78 Horus I Shemu 20 9 259.33 291 231 phenomena in CC, one should realize that only a few events relating to celestial objects, however important they were considered to be, could have determined an riods in CC are those of the regular brightness changes of extensive and significant set of periodic prognoses. For a variable star (Jetsu et al. 2013, p9). example, the heliacal rising of a star is a yearly event, and may affect the prognosis of one day. Thus, it can not be discovered from the calendars by period analysis. The 2.2 Methods synodic periods of planets, because of their length, are also out of the question (Jetsu et al. 2013, p13). Except We relate CC texts to astronomical events by the phase for the Moon, the only other detectable astronomical pe- angles calculated from the days that the texts refer to 236 S. Porceddu et al., Algol as Horus in the Cairo Calendar

Table 3. “GGG” prognosis texts mentioning Horus, “Wedjat”, “Sakhmet”, “Seth” and “Osiris”. These five Seth or Osiris. Notations are as in Table 1, except that all deities are the most relevant ones regarding the two values are in the order of increasing Θ . Moon prominent myths “The Destruction of Mankind” and “The Contendings of Horus and Seth” that will be de- SW Month D M g(D,M) ΘAlgol ΘMoon Horus I Shemu 1 9 240.33 51 0 scribed in Sect. 4.7. Horus II Shemu 1 10 270.33 240 5 “Horus”, etymologically the distant one, was a sky Osiris II Shemu 1 10 270.33 240 5 god or stellar god associated with kingship and order. Osiris III Peret 6 7 185.33 303 51 Krauss (2016, p137-141) suggests that Horus was origi- Seth IV Akhet 9 4 98.33 114 73 nally a stellar god who later became subordinated to so- Horus I Shemu 7 9 246.33 88 73 Osiris IV Akhet 11 4 100.33 6 98 lar mythology. Already the earliest texts regarding Horus Horus II Akhet 14 2 43.33 6 124 describe him as the “Foremost star of the sky”. In the Osiris II Akhet 16 2 45.33 259 149 Pyramid Texts, a younger Horus is called Horus-son-of- Seth IV 13 12 342.33 335 161 Isis and is distinguished from the elder Horus (Haroeris). Shemu According to Krauss these would be Venus as the morning Osiris IV 13 12 342.33 335 161 star and the evening star. On one hand the connection of Shemu Horus I Akhet 18 1 17.33 322 168 the planet Venus, usually considered feminine, with the Horus III 15 11 314.33 38 180 king would be unique to Egypt. Yet Venus was certainly Shemu associated with Benu, the divinity who in the creation Osiris II Peret 17 6 166.33 63 180 myth laid the first stone benben, which became Earth, Horus IV 19 12 348.33 13 234 upon the primal sea. Horus’ rival god Seth was the em- Shemu Horus III Akhet 24 3 83.33 19 251 bodiment of disorder, identified in some sources with the Horus III Peret 23 7 202.33 291 258 planet Mercury, the other inner planet besides Venus. In Horus I Akhet 27 1 26.33 19 278 the most commonly known mythological narrative Osiris, Seth I Akhet 27 1 26.33 19 278 the father of Horus, was killed by Seth. Horus avenged Horus III Akhet 27 3 86.33 38 287 his father and the resurrected Osiris was to be considered Seth III Akhet 27 3 86.33 38 287 the patron of the dead, especially the dead king (Meltzer Horus III Akhet 28 3 87.33 164 300 Osiris III Akhet 28 3 87.33 164 300 2001, p119-120). Sakhmet was a lion goddess associated Horus III Akhet 29 3 88.33 291 312 with the scorching, destructive power of the Sun, also Seth III Akhet 29 3 88.33 291 312 called Wadjet or the Eye of Horus (Leitz and Budde 2003, Osiris III Peret 28 7 207.33 202 319 p361) and (Jong 2001, p512-513). Horus III Peret 1 7 180.33 32 351 While Jetsu and Porceddu (2015) studied some texts mentioning “Horus”, “Sakhmet” or “Seth”, and used the (Eqs. 1-4). We select four samples from CC (Tables 1-4) text from the CC translation of Bakir (1966), we study all which give us two lists of CC text passages (Lists 1 and prognosis texts mentioning any of the above mentioned 2). five deities, and we use our own translations of these CC Recently, a statistical study was made of the occur- texts. rence of 28 different SWs in the CC prognosis texts (Jetsu We calculate the “Egyptian days” for these SWs from and Porceddu 2015, p3). The occurrences of individual NE = 30(M − 1) + D, (1) SWs were studied separately. The lucky prognosis texts mentioning “Horus” were studied in greater detail, and a where M is the month and D is the day of the date in few unlucky texts mentioning “Sakhmet” or “Seth”. Those CC (Jetsu et al. 2013, Table 1). The SW dates are trans- texts were taken as such from the CC translation of Bakir formed (Jetsu and Porceddu 2015) into time points with (1966). the relation We downloaded these SW data (Jetsu and Porceddu 2015, p1) from the Dryad database3, where the respective t = t(D,M)= NE − 1+0.33. (2) ASCII file-name is data2.txt. This gave us the dates when We use the notations g = g(D,M) = t(D,M) and s = any particular SW is mentioned in CC. Here, we con- s(D,M)= t(D,M) for the time points of GGG and SSS centrate on the following five particular SWs: “Horus”, prognosis days, because these two prognosis samples were analysed and studied separately (Jetsu et al. 2013; Jetsu 3 http://dx.doi.org/10.5061/dryad.tj4qg and Porceddu 2015). S. Porceddu et al., Algol as Horus in the Cairo Calendar 237

o Table 4. “SSS” prognosis texts mentioning Horus, Seth Ma ≡ ΘMoon =0 = Full Moon or Osiris. Notations are as in Table 3. o Mb ≡ ΘMoon = 90 = Between Full and New Moon o Mc ≡ ΘMoon = 180 = New Moon SW Month D M s(D,M) Θ Θ Algol Moon Md ≡ Θ = 270o = Between New and Full Moon Horus IV Peret 5 8 214.33 6 44 Moon Seth II Akhet 12 2 41.33 114 100 All D, M, g(D,M), s(D,M), ΘMoon and ΘAlgol val- Seth III Akhet 13 3 72.33 69 117 ues of “Horus”, “Wedjat”, “Sakhmet”, “Seth” and “Osiris” Osiris III Akhet 13 3 72.33 69 117 are given in Tables 1-4. Osiris III Akhet 14 3 73.33 196 129 Horus III 11 11 310.33 253 132 We study all CC passages mentioning “Horus”, Shemu “Wedjat”, “Sakhmet”, “Seth” and “Osiris”. These pas- Seth IV 11 12 340.33 82 137 sages give the date first, inscribed in red colour. Then Shemu follow the daily prognoses, and the descriptive prognosis Osiris I Peret 14 5 133.33 215 139 text. The time point for every date is unambiguous, be- Seth III Akhet 18 3 77.33 341 178 × Seth III Peret 17 7 196.33 253 185 cause the structure of CC is regular, 12 30 days (Eqs. 1 Seth IV Peret 17 8 226.33 82 190 and 2). Hence, the time points for the prognoses, the SWs Osiris IV Akhet 19 4 108.33 297 195 and the prognosis texts describing the actions of deities Seth II Akhet 20 2 49.33 44 197 are also unambiguous. 4 The exact dating of the CC, as a Horus I Shemu 20 9 259.33 291 231 historical document, is irrelevant in the current analysis, Horus I Akhet 26 1 25.33 253 266 like it also was in the previous statistical studies (Jetsu Seth I Akhet 26 1 25.33 253 266 Seth IV Peret 24 8 233.33 246 275 et al. 2013; Jetsu and Porceddu 2015). Adding any arbi- trary constant to the time points of Eq. 2 shifts all phase angles Θ with the same amount, e.g. the ΘAlgol values of For any period value P , the phases of t are all passages of List 1. This is the reason why our results based on Lists 1 and 2 do not depend on such shifts (FAQ φ = FRAC[(t − t )/P ], (3) 0 2). where FRAC removes the integer part of (t − t0)/P and The number of passages mentioning some SWs is very t0 is the zero epoch. In other words, FRAC removes the small (e.g. n = 3 for “Sakhmet” in Table 2). It is there- number of full P rounds completed after the zero epoch fore necessary to explain how can we draw reliable sta- t0. The phase angles are tistical conclusions from the analysis of such data (FAQ 3). Firstly, the periods PAlgol and PMoon were detected Θ = 360oφ. (4) from large samples of over five hundred time points and Jetsu et al. (2013) discovered two significant periods, these periodicities were extremely significant (Jetsu et al. PAlgol = 2.850 and PMoon = 29.6 days, in the lucky 2013). For example, the period PAlgol reached critical lev- prognoses of CC. In their next study, they determined els Q∗ < 0.0001 (Jetsu et al. 2013, Table 7), i.e. the prob- these two ephemerides (Jetsu and Porceddu 2015) for the ability for this period being real was 1−Q∗ > 0.9999. Sec- phases of Eq. 3 ondly, the ephemerides of Eqs. 5 and 6 are also very reli- able, because they were determined from the same large t =0.53,P = P =2.850 (5) 0 Algol data samples (Jetsu and Porceddu 2015). Thirdly, al- t0 =3.50,P = PMoon = 29.6 (6) though the Rayleigh test significance estimates computed The phase angles Θ (Eq. 4) computed with the by Jetsu and Porceddu (2015, their Eq. 8: Qz) for some ephemerides of Eqs. 5 and 6 are hereafter denoted with smaller samples were not reliable, the binomial distribu- tion significance estimates for the very same samples were ΘAlgol and ΘMoon, respectively. We also use their eight abbreviations (Jetsu and Porceddu 2015, p6-7) certainly reliable (their Eq. 13: QB). Fourthly, the order of the passages in Lists 1 and 2 is the same (i.e. unam- o Aa ≡ ΘAlgol = 0 = Mid-epoch of Algol’s secondary biguous) for any arbitrary epoch t0 in Eqs. 5 and 6. For eclipse these four reasons, the phase angles computed from the o Ab ≡ ΘAlgol = 90 = Between mid-epochs of sec- ondary and primary eclipse o Ac ≡ ΘAlgol = 180 = Mid-epoch of Algol’s primary 4 The calendar dates are fixed and known even if the texts or eclipse the deities mentioned in these texts were not studied at all. o Ad ≡ ΘAlgol = 270 = Between mid-epochs of primary The deities mentioned in these texts do not determine the dates and secondary eclipse (FAQ 1). 238 S. Porceddu et al., Algol as Horus in the Cairo Calendar

ephemerides of Eqs. 5 and 6 can be used just like the time passages are discussed in Sect. 4.8. We highlight the un- given by an accurate modern clock. For example, such a lucky CC prognosis text passages with red colour, to visu- clock shows that most people go to sleep before midnight. ally distinguish these unlucky texts from the lucky ones, It is irrelevant if only a few (small n), or many (large n), since red colour is also used in CC for writing the prog- people go to sleep. Rearranging the texts of CC into the nosis “bad” and the name of the feared serpent creature increasing order of ΘAlgol may show what the authors of Apep. Other texts in papyrus Cairo 86637 display an even CC wrote about “Horus” at different phases of the cycle more varied use of red colour for the sake of emphasis and (FAQ 4). captioning (Bakir 1966, p7). It is possible to dispute our translations of the texts of The ΘAlgol values of the g(D,M) and s(D,M) time Lists 1 and 2 (FAQ 5), but these translations are relevant points of List 1 are shown separately in Figures 1 and 2. only for the two Arguments VII and VIII, i.e. the validity The relative positions of Algol A (white disk) and Algol of the eight other arguments in Sects. 4.1-4.10 does not B (black disk) at points Aa, Ab, Ac and Ad are shown depend on these translations. In these translations, we in four small boxes of Figures 1 and 2. For a naked eye have used the English translation by Bakir (1966) and observer, Algol’s brightness appears constant, except for the German translation by Leitz (1994), and his tran- the 10 hour dimming during ΘAlgol values marked with script of the original papyrus, as well as photos of the a thick curved line centered at Ac. These eclipse phase o o original papyrus. For example, all 460 SW identifications angles are in the interval 153.7 ≤ ΘAlgol ≤ 206.3 . Time by Jetsu and Porceddu (2015) and Leitz (1994) were iden- runs in the counter-clockwise direction. One complete or- tical, and here we use the same SW list. Some words or bital round PAlgol is Aa → Ab → Ac → Ad → Aa. sentences could be translated differently, but that would The lucky time points g(D,M) of SWs having o o d not change the general description of the course of events −90 < ΘAlgol < 90 amplify the PAlgol = 2. 85 signal in the translated passages of Lists 1 and 2. Also the prog- (Jetsu and Porceddu 2015). The closer a ΘAlgol value of o noses, which were taken as such from Leitz (1994), are some g(D,M) is to the point Aa at ΘAlgol =0 in Figure independent of any translation nuances. 1, the greater is the amplifying impact of this g(D,M) A non-parametric method, the Rayleigh test, has value on the PAlgol signal. A previous study by Jetsu and been applied to the series of n time points t1,t2,...tn Porceddu (2015) showed that of all their 28 SWs, “Horus” of CC (Jetsu et al. 2013; Jetsu and Porceddu 2015). had the strongest impact on the PAlgol signal. The other Here we study the SWs and the CC texts of these time remaining SWs having an impact on the PAlgol signal were points. These time points are circular data and a “non- “Re”, “Wedjat”, “Followers”, “Sakhmet” and “Ennead”. parametric” method means that there is no model. It has been suggested that we should apply a χ2-test to our data (FAQ 6). This “parametric” test could be applied if the 3.2 Moon: Horus, Seth and Osiris format of our data were y(t1),y(t2),...y(tn), i.e. a time passages of List 2 series, like magnitudes of a star as function of time. The 2 n 2 2 value of this test statistic is χ = Pi [y(ti) − g(ti)] /σi , The lucky and unlucky days of CC texts mentioning where g(ti) is the value of the model at ti and σi is the “Horus”, “Seth” or “Osiris” are given in Tables 3 and error of y(ti). However, we can not apply this χ2-test, 4. Our translations of CC passages mentioning “Horus”, because we have no time series, no model and no errors. “Seth” and “Osiris” are rearranged into the order of in- creasing ΘMoon in List 2 of Appendix D. We discuss these passages in Sect. 4.8. 3 Results The ΘMoon values of the g(D,M) and s(D,M) time points of List 2 are shown in Figs 3 and 4. The appear- ance of the lunar disk at points Ma, Mb, Mc and Md is 3.1 Algol: Horus, Wedjat and Sakhmet illustrated in four small boxes of Figures 3 and 4. Again, passages of List 1 time runs in the counter-clockwise direction, where one complete synodic lunar month PMoon is Ma → Mb → Mc The lucky and unlucky days of CC texts mentioning → Md → Ma. “Horus”, “Wedjat” or “Sakhmet” are given in Tables 1 The time points g(D,M) of SWs with phase angles o d and 2, respectively. We rearrange our translations of CC ΘMoon close to ΘMoon = 0 amplify the PMoon = 29. 6 passages of “Horus”, “Wedjat” and “Sakhmet” into the signal. Jetsu and Porceddu (2015) showed that of all their order of increasing ΘAlgol in List 1 of Appendix C. These 28 SWs, “Earth” and “Heaven” had the strongest im- S. Porceddu et al., Algol as Horus in the Cairo Calendar 239

Figure 1. ΘAlgol phase angles of lucky time points of Table 1. Time runs in the counter-clockwise direction on this circle. Epochs Aa, Ab, Ac and Ad are separated by 90 degrees and they are denoted with dotted straight lines. The relative locations of Al- gol A (white disk) and Algol B (black disk) at these four epochs are shown in the small boxes. Primary and secondary eclipses of Algol occur at Ac and Aa, respectively. The thick curved line centered at Ac outlines the phase angles of the 10 hour primary eclipse of Algol o o at 153.7 < ΘAlgol < 206.3 . The phase angle values ΘAlgol of “Horus” (closed squares), “Wedjat” (open squares) and “Sakhmet” (closed triangles) are denoted with continuous straight lines.

pact on the PMoon signal, i.e. their lucky prognoses were ever, the order of these “Horus” texts is different when close to the Ma point. This is natural because lunar feast rearranged in the order of increasing ΘAlgol or ΘMoon. dates where often described as feasts in “Earth” and in “Heaven” (FAQ 4). The other SWs connected to PMoon were “Busiris”, “Rebel”, “Thoth” and “Onnophris” (Jetsu 4 Discussion and Porceddu 2015). The unlucky time points s(D,M) of two SWs, “Seth” and “Osiris”, pointed to the opposite di- o We present one argument about CC in the end of each rection, ΘMoon = 180 . The CC texts of “Seth” strongly o Sect. 4.1-4.10. indicated that ΘMoon = 180 coincided with the New o Moon. Hence, it was concluded that ΘMoon = 0 ≡ Ma represented the Full Moon (Jetsu and Porceddu 2015). 4.1 Measuring night-time with hour-stars These connections are hardly surprising either because “Osiris”, also called “Onnophris”, was identified with the At the night-time in ancient Egypt, time was traditionally Moon during the New Kingdom (Kaper 2001, p480-482). measured from the positions of hour-stars. “Thoth” was another known lunar god (Leitz and Budde The ancient Egyptian day was split into daytime and 2003). “Busiris” was the place of origin for “Osiris”. night-time, both with 12 hours. Time was counted us- “Rebel” is often synonymous for “Seth” (Leitz 1994, p91). ing shadow clocks by day, and star clocks or water clocks Note that the texts mentioning “Horus” are included by night. The Egyptian “hour-watcher”Nwas a special- in both Lists 1 and 2, because the name “Horus” appears ized scribe whose job was to observe various hour-stars, in both mythical narratives of Sects. 4.7.1 and 4.7.2. How- i.e. clock stars whose positions began and ended the night hours (Figure 5). More specifically, a text previ- 240 S. Porceddu et al., Algol as Horus in the Cairo Calendar

Figure 2. ΘAlgol of unlucky time points of Table 2. Notations as in Figure 1.

Figure 3. ΘMoon of the lucky time points of Table 3. Time runs in the counter-clockwise direction on this circle. Epochs Ma, Mb, Mc and Md are separated by 90 degrees and they are denoted with dotted straight lines. The phases of the Moon are shown in the small boxes. The Full and the New Moon occur at Ma and Mc, respectively. The phase angle values ΘMoon of “Horus” (closed squares) “Seth” (open triangles) and “Osiris” (closed circles) are denoted with continuous straight lines. S. Porceddu et al., Algol as Horus in the Cairo Calendar 241

Figure 4. ΘMoon of the unlucky time points of Table 4. Notations as in Figure 3. ously known as “The Cosmology of Nut” whose title was stars. The hour-watcher facing south might have utilized deciphered by Lieven (2007) to be “The Fundamentals a plumb and a sighting device to determine when the of the Course of the Stars” informs us that stars were given star is in exactly the right position and announce traditionally observed when in positions of the “culmi- the closing of the hour. If the hour-watchers were posi- nation”Nupon the first hour of the night (transit of the tioned 2-3 meters away from each other, the slow rotation meridian between the eastern half of the sky and the of the night sky would have provided a 10-15 minute dif- western half of the sky), “heliacal setting”N and “heli- ference between the marked positions (Leitz and Thissen acal rising”N(Clagett 1995, p56-65). Tabulated positions 1995, p33). According to Lull and Belmonte (2009, p165) of hour-stars marked the closing of each night hour. One it is more likely that the figure that had been interpreted approximation for the length of an Egyptian night hour as an hour-priest would rather be a divinity associated was 40 minutes (Leitz and Thissen 1995, p133). with time-keeping, leading to revised ideas regarding the The Ramesside Star Clocks from the tombs of Ram- direction of the observations: even some constellations of ses VI, Ramses VII and Ramses IX show an even more the northern half of the sky could have been used in complex arrangement of hour-stars (Clagett 1995, p56- this method of time-keeping. The references to the ob- 65). Each table consists of thirteen rows of stars. The servational practices of the hour-watchers are scarce and first row stands for the opening of the first night hour known mostly from late period sources such as the inscrip- and the other twelve rows stand for the closing of each of tion on a statue depicting the astronomer Harkhebi and the twelve night hours. In the rows, a star is positioned a sighting instrument with inscriptions mentioning an as- in respect to a sitting human figure. Possible positions tronomer named Hor (Clagett 1995, p489-496) and (Pries are “upon the right shoulder”N, “upon the right ear”N, 2010, p10-26). However, it is safe to say that such prac- “upon the right eye”N, “opposite the heart”N, “upon the tices existed throughout Pharaonic history. The observing left eye”N, “upon the left ear”N, and “upon the left shoul- conditions of the hour-watchers were rather ideal, with der”N (Figure 5). The system was originally interpreted about 300 clear nights each year (Mikhail and Haubold as two hour-watchers opposite to each other on the roof of 1995, pD7). the temple precisely aligned to the line of the meridian. Algol is the 60th brightest star in the sky (Hoffleit These timing observations would have been necessarily and Jaschek 1991). At the latitude of Middle Egypt, o made towards south, because of the positions of the hour- φEarth = 26.6 , the never setting circumpolar stars have 242 S. Porceddu et al., Algol as Horus in the Cairo Calendar

Figure 5. Hour-watcher with a star chart from the tomb of Ramesses VI, 12th century BC. “Meridian” is “opposite the heart” mentioned in Sect. 4.1. Reprinted under a CC BY license @eng.wikipedia.org.

o o declinations δStar > 90 − φEarth = 63.4 . The declina- to obtain accurate timing from the minor changes in their tions of stars that never rise above horizon are δStar < positions. Stars below horizon can certainly not be used o o φEarth − 90 = −63.4 . Circumpolar stars are not ideal as hour-stars. If the circumpolar stars and the stars below hour-stars, because they never rise or set. Furthermore, horizon are excluded, Algol was the 56th brightest star at o their angular motion within a limited area around the ce- φEarth = 26.6 in 1224 B.C. However, if a star culminates lestial pole is not ideal for measuring time. It is not easy in the south below an altitude of a = 10o, its brightness S. Porceddu et al., Algol as Horus in the Cairo Calendar 243 decreases about one magnitude due to atmospheric ex- day periods, where the timing of the hours fluctuated tinction and it can be observed only for a short time even even 55 minutes. However, this model seems to have been in ideal observing conditions. Such a star is not a suitable outdated by the time it was used in the decoration of hour-star. A star that sets 10o (or less) below horizon in Ramesside tombs, so the later developments of the system the north is neither an ideal hour-star, because it rises remain unknown (Leitz and Thissen 1995, p132). and sets nearly at the same location, and its brightness No-one can recognize a single hour-star in the sky decreases close to the horizon due to extinction. Using without comparing its position to the positions of other o o the limits −53.4 < δStar < 53.4 , makes Algol the 51st bright stars in its vicinity. For the sake of consistency, brightest star in the Middle Egyptian sky in 1224 B.C. we introduce our own precise concept: “hour-star pat- These declination limits of ours are conservative, because tern”. Such a pattern contains one hour-star used by the many other stars culminating in the north are useless for scribes, and all bright stars that they used to identify this time keeping, and extinction influences the comparison of hour-star. Using only two stars per one hour-star pat- the brightness levels between Algol and the stars always tern would not have provided any recognizable pattern. remaining close to the horizon. This raises Algol much Therefore, the number of stars per each hour-star pattern higher than the 51st best in the list of suitable bright must have been at least three, or probably more. This hour-stars (FAQ 7). means that the Ancient Egyptians must have observed at Algol’s equatorial coordinates were right ascension least 24 × 3 = 72 bright stars, and in this case the vi- o o m αAlgol = 1 and declination δAlgol = 25 in 1224 B.C. sual brightness of the 72th brightest star was about 2. 5 which gives the following ecliptic coordinates, longitude in 1240 B.C. Thus, it is certain that the 51st brightest o o m λAlgol = 11 and latitude βAlgol = 22 . The ancient star Algol (2. 12) with an ideal position in the night sky cultures used the latter coordinate system based on the was included into some hour-star pattern (FAQ 7). The yearly motion of the Sun. Algol was located very close to names of hour-stars in the Ramesside star clocks include the vernal equinox and this ecliptic plane. If the timing for example various different body parts and equipment observations were made towards south, then the bright of the Giant, the Bird and the Hippopotamus, suggest- stars in the ecliptic plane were the most suitable hour- ing that the stars were members of a known constellation star candidates (Clagett 1995, p2-56), (Wells 2001b, p145- (i.e. an hour-star pattern). According to Belmonte et al. 150) and (Böker 1984). This location of Algol in the sky (2009, p157-194), a complete set of constellations formed raises it very high in the list of suitable bright hour-stars the Egyptian celestial diagram, i.e. every star belonged (FAQ 7). Furthermore, Algol culminated at the altitude to some constellation. of a = 88o, and this made it an ideal star for measuring Unlike Astronomy, Egyptology is not an exact sci- time. ence and few questions can be answered with absolute One modern hour equals 15 degrees in the equatorial certainty. For our ten arguments I-X presented in Sects. plane, and therefore the required minimum number of 4.1-4.10 it is not important if Algol was an actual hour- hour-stars for covering the entire sky is at least 24. The star or only a member of some hour-star pattern or related earliest known star clock scheme, the so-called diagonal constellation (FAQ 7). Algol has not yet been unambigu- star clock, describes 36 decans (Leitz and Thissen 1995, ously identified in any hour-star lists because only the p63). For a ten-day week, 12 of the decans are tabulated names of Sirius, Orion and the Plough have reached a marking the beginnings and ends of the hours. Because widespread consensus among egyptologists. Algol (β Per- the sidereal day is about four minutes shorter than the sei) is the second brightest star in the modern constella- solar day, these stars reach their positions four minutes tion of Perseus. Egyptologists have presented their own earlier every consecutive night. After ten days the stars differing identifications of the represented stars with ac- occupy their positions about 39 minutes earlier, so in the tual stars so it is difficult to say which decan or group tabulation of decans for the next week each of the stars would have included Algol (Belmonte et al. 2009, p161- "works" one hour earlier. The concept of the hour was 162), (Böker 1984) and (Conman 2003). Lull and Bel- relative as its beginning was allowed to fluctuate about monte (2009, p157-158) claim to have uncovered nearly 35 minutes by the end of each week. The later Ramesside three quarters of the Egyptian firmament by deciphering star clocks are comprised of a system of 46 individual stars the star names of aforementioned tomb of Senenmut, the observed in positions such as “upon the right shoulder”, clepsydra (water clock) of Amenhotep III and the circular “upon the right ear”, etc. as in our Figure 5 (Leitz and zodiac of the temple of Hathor at Dendera, which is from Thissen 1995, p120). These positions were intended for Late Period and already incorporates Mesopotamian and better accuracy but the known tables were given for 15- Greek influences. According to them, the ancient Egyp- 244 S. Porceddu et al., Algol as Horus in the Cairo Calendar tian constellation of the Bird includes the modern constel- three millennia are almost obsolete in any quantitative lations Triangulum and Perseus but there is no precise approach despite the culture’s special attention to the identification of the individual stars of the Bird. Böker Sun, the Moon, the planets and the stars as divine enti- (1984) suggested that the correct reading for the decan ties (Neugebauer 1951, p71-72). The phases of the Moon Khentu, a group of three stars, is the “snorting one”N. and the heliacal rising of Sirius played a part in deter- The decan is later depicted as a red-haired warrior with mining the date and time of New Year and several other fierce attributes reminiscent of Perseus in Greek mythol- important festivals. ogy. The decan is also known as “the lower Khentu”N, and In ancient Egypt, the scribal professions were the mentioned in the decan lists of the Astronomical ceiling most valued ones, as the entire functioning of the highly of the tomb of Senenmut (ca. 1473 B.C.), tomb of Seti I developed culture and state with its complex bureaucracy (1313-1292 B.C.) and the Osireion, a temple in Abydos was based on written communication (Shaw 2012, p24- dated to the time of Seti I (Neugebauer and Parker 1960, 38). Many of the professional scribes had several titles em- p23-26). phasizing their specialized knowledge (Clagett 1989, p18- The number seven seems to carry plenty of mytho- 24), such as “physician”N, “healer”N, “hour-watcher” (as- logical connotations for the Egyptians, such as the seven tronomer who observed stars for timekeeping purposes) failed attempts of “Seth” to lift the foreleg into the heav- and “mathematician”N. ens (Leitz 1994, p28). It is reminiscent of the various Beside the religious background, the scribes had names of the Pleiades, a distinct open cluster of bright plenty of social, political and personal motivation to per- stars located near Perseus (i.e. Algol), known for example form their job with utmost expertise. Many scribes re- as Seven Sisters, Starry Seven and Seven Dovelets (Allen ceived the title of “king’s favourite” during their life- 1899, p391-403). Pleiades may have been connected to the time and such persons were among the most high ranking “Followers” or the “Ennead” which were both connected members of the Egyptian society (Clagett 1989, p195). to PAlgol in CC (Jetsu and Porceddu 2015, p14-15). What would have been the ancient Egyptian scribes’ A list of decan deities in papyrus Carlsberg I men- interest in the behaviour of a variable star? Knowing the tions certain stars that cause “sickness”Nin fish and birds, period and the phase of the Moon was important for while CC speaks of "a star with bitterness in its face". Ac- regulating the religious festivities but the scribes would cording to Leitz (1994, p307), “bitterness”Nis the name of also have paid attention to any unexpected changes in a sickness that plagued the Egyptians. Decans in the in- the observed hour-star patterns. The hour-watchers’ ac- scription 406 of the temple of Esna are portents of death tivity required the mapping and measuring of the helia- to the "rebel" (von Lieven 2000, p48). Thus, even with- cal rising and setting, as well as the meridian transit of out knowing which stars exactly they referred to in these stars (Magli 2013, p55). The average width for a suit- passages, we may conclude that the ancient Egyptians able ancient Egyptian hour-star pattern would have been strongly believed in stars influencing the lives of men. about one hour in modern right ascension, i.e. 15 degrees. Argument I: For thousands of years, the “hour- Thus, during every year, Algol’s hour-star pattern deter- watchers” practiced the tradition of timekeeping by ob- mined the beginning of the night during half a month serving hour-stars. If Algol was not an hour-star, it cer- (∼ 15o/360o), the epoch of midnight during another half tainly belonged to some hour-star pattern or related con- a month, and the end of the night during yet another stellation. half a month. During thousands of years of timing ob- servations, the discovery of Algol’s variability would have been most probable during these particular time intervals 4.2 Crucial timing of nightly rituals of every year (FAQ 7). It is essential to note that the professional class of Proper timing was considered crucial for the efficacy of scribes was responsible for both astronomical observations nightly religious rituals. and religious traditions. To be involved in the science of Astronomy is often considered to be one of the old- Astronomy (e.g. hour-watching) was also to be involved est sciences practiced by mankind despite ancient star in the priesthood (e.g. nightly rituals) (Shaw 2012, p11- observing being carried out for the benefit of religious 16). To properly observe the ritual cycle and recite the practices. Babylonians were probably the first people to magical words at the exactly right time was of foremost make systematic notes of the Moon and the planets and importance to the Egyptian priests, since it was a mat- also to perform calculations of their celestial motions. ter of life and death (Assmann and Lorton 2001, p64-68). As opposed to this, ancient Egyptian records that span The hour-stars were used for this exact timing that was S. Porceddu et al., Algol as Horus in the Cairo Calendar 245 crucial for keeping cosmic order (Clagett 1989, p195) and brightening that lasted for another five hours. This entire (Magli 2013, p2). During the night, the Sun was con- 10 hour eclipse event could be observed during a single sidered to sail across the underworld where the prayers night, but that was rare event, because it occurred only or incantations of the priests opened the gates of the un- every 19th night. Algol’s hour-star pattern change was so derworld and appeased the terrible guardians of the gates noticeable that the priests on duty as hour-watchers could (Wiebach-Koepke 2007, p37-58). If everything went abso- hardly have missed this event. For the hour-watchers, it lutely right, the Sun was reborn on the 12:th hour of the would have been useful to communicate among them- night. Any failure by the priests in observing the nightly selves the knowledge about the strange behavior of this rituals would mean running a risk of the Sun not rising hour-star pattern and there is a good possibility, consider- the next morning (Assmann and Lorton 2001, p68-73). ing the diligent scribe mentality of Egyptian officials, that The consequential purpose of astronomical observa- they would have made written notes about the times of tions was “religious astronomy” (von Lieven 2000, p188). the eclipses. Any unpredictable change in the hour-star patterns ob- The modern constellation of Perseus is one of the eas- served by the scribes would have been a shock. The ritual iest to perceive. It occupied a prominent position high in activity of the ancient Egyptian priesthood functioned for the ancient Egyptian night sky, because the maximum al- the very purpose of maintaining the known universe in a titude of Algol was 88 degrees. Algol is the brightest mem- stable condition in order not to plunge into chaos. They ber of another ancient constellation of four stars which needed to use all their resources to keep “Maat”N, the was already recognized by authors like Vitruvius (Vitru- cosmic order (Magli 2013, p2). If they found out that a vius and Morgan 1960, p266-267) and Ptolemy (Ptolemy star is variable in brightness, observing its cycle would et al. 1915, p31). The other three stars are π Per (4.m7), most certainly have gained their extra attention and in- ω Per (4.m6) and ρ Per (3.m4−4.m0). During the primary tellectual effort. eclipses, the brightness of Algol falls from 2.m1 to 3.m4, Argument II: Proper timing of the nightly religious i.e. these other three stars never appear to be brighter rituals relied on the fixed hour-star patterns. than Algol. The shape of this constellation resembles a diamond and it was therefore called the Head of Gorgon or the Head of Medusa (Allen 1899, p332) in the Hellenis- 4.3 Constellation change tic culture. The angular separation between Algol and the other three stars is less than two degrees, and this constel- Any unpredictable change in the fixed and known hour- lation is therefore ideal for detecting variability because star patterns would have been alarming. A naked eye ob- atmospheric extinction does not mislead brightness com- server witnesses a radical hour-star pattern change during parisons even at low altitudes close to the horizon. At its Algol’s eclipse. brightest, Algol visually dominates this diamond shaped The naked human eye can detect brightness differ- constellation, because it is clearly much brighter than the ences of 0.1 magnitudes in ideal observing conditions. other three stars. Hence, a naked eye observer can easily Hence, naked eye eclipse detection is theoretically pos- notice the significant constellation pattern change during sible for 7 hours when Algol is more than 0.1 magnitudes Algol’s eclipse. Wilk (1996) suggested that from this may dimmer than its brightest suitable comparison star γ An- have arisen the myth of the Medusa losing its head. dromedae (see Jetsu et al. 2013, their Figure 5a). For 3 In principle, other variable stars besides Algol, like hours, Algol is also dimmer than its other five suitable the disappearing and reappearing Mira, also called Omi- comparison stars ζ Persei, η Persei, γ Persei, δ Persei and cron Ceti, might also have been discovered by the ancient β Trianguli. The detection of Algol’s eclipse is easy during Egyptians. However, the eleven month period of Mira is this 3 hour time interval. so long that it can not be rediscovered with statistical With PAlgol = 2.850 = 57/20 days, these op- methods in CC (Jetsu et al. 2013, p9, see Criterion C2). portunities for easy detection follow the sequence of Argument III: A naked eye can easily discover the “3+3+13=19” days (Jetsu and Porceddu 2015, p20-21). significant hour-star pattern change caused by Algol’s A plausible hypothesis is that the ancient Egyptians first eclipse. discovered the variability of Algol, like Montanari did in 1669, when they were observing Algol’s hour-star pattern. During primary eclipses, Algol lost its brightness gradu- ally for five hours until it was outshined by its six dimmer nearby comparison stars. The dimming was followed by a 246 S. Porceddu et al., Algol as Horus in the Cairo Calendar

PA . (a) PA . (b) Night-time eclipses (blue) =56 Night-time eclipses (blue) =52 Daytime eclipses (red) =70 Daytime eclipses (red) =73 z . z . z . z . z . z .

Figure 6. Mid-epochs of Algol’s primary eclipses. (a) The yearly mid-epochs of 56 night-time eclipses occurring ±5 hours at both sides of midnight with the period PAlgol = 2.850 days (blue circles). The red circles denote the 70 daytime eclipses. Note that only 20 circles are visible, because the 56 red or 70 blue circles overlap. The eclipse phase angles ΘP=19 are computed for the period P = 19 days. The values of the Rayleigh test statistic for these eclipse epoch time points with P = 19 days (Jetsu and Porceddu 2015, z in Eq. 7) are given for the night-time eclipses (znights), the daytime eclipses (zdays) and all eclipses (zboth). (b) The same as in (a), except that the current period value, PAlgol = 2.867 days, is used.

4.4 “3+3+13=19” and “19+19+19=57” watchers began to make notes of the eclipse epochs, the days eclipse rules “3+3+13=19” days eclipse cycle would have been dis- covered first, then later the “19+19+19=57” days eclipse Algol’s night-time eclipses followed the regular cycle. The first regularity is easier to discover, because all 3+3+13=19 and 19+19+19=57 days cycles with PAlgol = Algol’s night-time eclipses follow this “3+3+13=19” cy- 2.850 = 57/20 days. (Jetsu and Porceddu 2015). cle with PAlgol = 2.850 = 57/20 days. The second cycle If an eclipse first occurred in the end of the night, of “19+19+19=57” days is more difficult to discover, be- then after three days the next eclipse occurred close to cause it requires the measurement of the nightly shifts of midnight. After another three days the next eclipse oc- these night-time eclipses within the “3+3+13=19” cycle. curred in the beginning of the night. After these three Although the ancient Egyptians had no way of knowing eclipses, it took thirteen days, before the next eclipse was that Algol’s eclipses also happened during daytime, their observed, i.e. the first eclipse in the end of the night was long-term eclipse records may have eventually led to the repeated again (Jetsu and Porceddu 2015). This is the discovery of this 57/20 days ratio. “3+3+13=19” days rule, i.e. a sequence of three night- Simulations have shown that modern period anal- time eclipses was repeated every 19 days. The midnight ysis would rediscover the 2.850 days period in CC, if eclipses, when both the dimming and the brightening of the scribes had recorded nearly all observed night-time Algol could be observed during the same night, occurred eclipses (Jetsu et al. 2013). The fact that the 19 days at 19 days intervals. Coincidence or not, the CC prog- period is also present in these data (Jetsu et al. 2013) nosis of the first day of every month is GGG and the confirms that only the night-time eclipses were used in prognosis of the 20th day of every month is SSS. These the construction of CC. This result can be deduced from two particular days of every month are separated by the Figure 6a. It is highly unlikely that the ancient Egyptians “3+3+13=19” days eclipse cycle. knew that Algol’s eclipses also occurred at daytime, be- With the period of PAlgol = 2.850 = 57/20, eclipses cause these events could not be observed. If an eclipse separated by 57 days would have occurred at exactly the occurred at the daytime, then no eclipse was observed on same time of the night. This is the “19+19+19=57” days the previous night or the next night. However, this ab- rule, i.e. this entire 57 days eclipse sequence kept on re- sence of night-time eclipses could be observed. This ab- peating itself over and over again. For this reason, there sence was observed in 16 nights of every 19 days cycle. are only 20 small blue or red circles (night-time or day- Our Figure 6a shows that there are two plausible alterna- time eclipses) in Figure 6a, although this figure shows tives that exclude each other. Either the presence (Figure all 126 eclipses occurring during 360 days. If the hour- S. Porceddu et al., Algol as Horus in the Cairo Calendar 247

6a: znights = 27.8) or absence (Figure 6a: zdays = 22.8) the occurrence of lunar eclipses (Pannekoek 1989, p57- of night-time eclipses was used as a criterion for selecting 62). Detailed long-term records were kept of these events. the lucky prognoses connected to Algol’s variability. In Somewhere between 750 and 650 B.C. there was a more other words, if the ancient Egyptians had used both the or less complete record of the observed eclipses and by night-time and the daytime eclipses in the construction of fairly basic analysis it was found out that within 223 lu- CC, this would have erased the 19 days signal completely nar months there were 38 eclipse possibilities. Also these away from CC (Figure 6a: zboth = 0.0). The alternative phenomena always occurred in a series of four, five or six that the absence of night-time eclipses was used in assign- consecutive lunar eclipses. A theory of the past and fu- ing lucky prognoses is more probable, because the lucky ture lunar eclipses, which was based on the table called prognoses mentioning “Horus”, “Sakhmet” and “Wedjat” “Saros-Canon”, emerged sometimes after 280 B.C. Brack- concentrate on the bright phases of Algol (Figure 1). This Bernsen and Steele (2005, p181) have argued that the alternative is later discussed in greater detail in Sect. 4.8 Babylonians may even have invented sophisticated meth- (principle I). ods to determine the anomalies (between 6 and 9 hours) The scribes seem to have applied a very accurate of the Saros cycle. Ancient Egyptians were also fluent in value for the synodic period of the Moon, 29.6 days, to arithmetic and geometric calculations and devised plenty correctly predict the lunar phases (Jetsu et al. 2013). of tabulations to aid in practical life (Clagett 1999, p24- If they intended a correct prediction of Algol’s eclipses 42) and (Rossi 2004, p57-60). Papyrus Carlsberg 9 reveals they would have also needed an accurate period value. that they used long-term observations to determine the Our Figure 6b shows how the “3+3+16=19” days cycle correct period of the Moon (Clagett 1995, p23-28). It has breaks down with the currently observed 2.867 days pe- also been shown that the PMoon value in CC was so ac- riod of Algol. Modern period analysis detects the 19 days curate it must have been determined from observations and the 2.850 days periods in CC, but it does not de- made over more than one year (Jetsu et al. 2013, p7). tect the current 2.867 days period of Algol (Jetsu et al. These two cases (Jetsu et al. 2013; Clagett 1995) con- 2013). Our Figure 6b confirms that if the period of Algol firm that the ancient Egyptians were capable of using in those days had been the same as the current period, long-term observations to determine the periods of ce- 2.867 days, there would be no signs of the 19 days period lestial objects. By the Late Period, the Egyptians were in CC (znights =0.4, zdays =0.3 and zboth =0.0). also familiar with the use of the Saros cycle of 223 syn- Argument IV: The scribes could have discovered Al- odic months to predict lunar and solar eclipses. Ptolemy’s gol’s 2.850 = 57/20 days period from long-term observa- commentators referred to these periods as having been tions of the regular 19 and 57 days eclipse cycles. used already by “the ancients” (Steele 2000, p88). Secondly, at about 400 B.C. the Chinese were using an astronomical calendar to predict the dates of lunar 4.5 Ancient Babylonian and Chinese lunar eclipses (Steele 2000, p175-178). This calendar made use eclipse prediction of a cycle of 135 months which includes 23 lunar eclipse possibilities. They approximated that eclipse possibilities The ancient Egyptian discovery of 2.850 = 57/20 days occur periodically every 5 and 20/23 months and counted ratio in Algol’s eclipses would resemble the ancient Baby- them arithmetically. The ancient Egyptians could have lonian and Chinese discoveries of the lunar eclipse cycle. used an analogous approach to Algol’s eclipses. Here, we discuss how these two analogous ancient astro- The alternating period changes of Algol are so small nomical cycle discoveries were made, and how the ancient (Biermann and Hall 1973) that they do not mislead long- Egyptians may have utilized a similar approach to observe term period determination based on naked eye observa- Algol’s variability. tions. However, the synodic period of the Moon varies Firstly, the process that may have lead to the ancient between 29.3 and 29.8 days in a year (Stephenson and Egyptian discovery of the periodicity of Algol’s eclipses Baolin 1991). Thus, Algol’s eclipses are far easier to pre- could have been analogous to the process which led to dict than lunar eclipses, because Algol’s period is con- the ancient Babylonian detection of the cycle in the lu- stant, while that of the Moon is not. The 2.850=57/20 nar eclipses. The unexpected occurrence of solar and lu- days ratio means that 20 eclipses of Algol occur during nar eclipses must have deeply impressed ancient civi- every 57 days cycle (Figure 6a). If the scribes performed lizations. The motivation for prognostications was obvi- long-term observations of these cycles, these observations ous. There is a description of how the Babylonians de- would have eventually revealed that all nine Algol’s night- termined the Saros cycle, 18 years and 11.33 days, in 248 S. Porceddu et al., Algol as Horus in the Cairo Calendar

time eclipses could always be observed within every 57 recorded the observed night-time eclipses into CC (3rd days cycle. method). There are three alternative methods of how the period of 2.850 days ended up into CC. We may never find out which one of these three methods was used. However, in 4.6 Indirect references to protect cosmic every alternative the scribes would have discovered the order eclipses of Algol, and recorded the period of these events. 1st method: The scribes might have calculated the nu- After the scribes had discovered Algol’s variability, it would have been attributed religious significance and de- merical value PAlgol = 2.850 days from long–term observations. scribed accordingly. 2nd method: The scribes may not have had any rea- Lack of direct references to Algol’s variability in an- son for even trying to calculate the actual period. cient Egyptian records raises questions. We may draw If they noticed that Algol’s three consecutive night- parallels to solar eclipses, which were experienced by time eclipses followed the 19 days cycle, while nine Egyptians during the New Kingdom and could not have consecutive night-time eclipses occurred in every passed unnoticed. Yet, these events are not mentioned di- 19+19+19=57 days cycle, these cycles would have rectly in written records (Smith 2012). The first plainly appeared extremely stable over very long periods of written Egyptian eclipse records are found in the demotic time. The minor nightly shifts in the epochs of the papyri Berlin 13147 + 13146 which date to the first cen- eclipses within individual 19 days cycles cancelled tury B.C. (Steele 2000, p85-91). Smith (2012) interpreted out within every 57 days cycle. The scribes may not references to solar eclipse events in New Kingdom texts even have noticed these minor nightly shifts within and concluded that astronomical events were described individual 19 days cycles, because the eclipses at indirectly by using religious terminology and the refer- the end of the night, close to the midnight or at the ence might even have been made deliberately obscure. In beginning of the night always returned back exactly Late Period demotic writings eclipses were mentioned and to the same moments of night after every 57 days described as fearsome and unlucky portents (von Lieven cycle. If the real period of Algol was 57/20=2.850 1999, p102). days, these 19 and 57 days cycles would have en- In general, ancient Egyptian scribes seem to have abled the scribes to foretell what would be observed avoided direct references to celestial events, because writ- in the sky. While the scribes may have recorded into ing was considered in itself to have a magical power that CC only the 19 or 57 days cycles in the night-time allows the scribe to communicate with the gods. This eclipses of Algol, modern period analysis confirms could be the reason why they avoided direct references that these rules worked perfectly only if the real pe- to the celestial events, i.e. the observed actions of divine riod of Algol was 57/20=2.850 days in those days. deities in the sky. The scribes would have avoided making Hence, the scribes have, although only perhaps un- direct textual references to the uncanny behaviour of Al- knowingly, also recorded the 57/20=2.850 days pe- gol in order to preserve cosmic order. Divine names that riod into CC. may have been related to Algol are various, depending on 3rd method: The scribes only used the observed epochs the context. In particular, the names “Horus”, “Wedjat” of night-time eclipses as such in the construction of and “Sakhmet” had similar phase angle ΘAlgol distribu- CC. This could be achieved even without ever solv- tions in Figures 1 and 2. We conclude that references to astronomical events are indirect but undoubtedly present ing a numerical estimate of PAlgol = 2.850 days, or without ever discovering the 19 and 57 days cy- throughout the whole CC text, not unusual for Egyptian cles. Also in this case, the scribes have unknowingly mythological texts in general (Leitz 1994, p285-286). recorded the 57/20=2.850 days period into CC. Argument VI: To avoid violating cosmic order, the scribes would have referred to Algol’s changes only indi- Argument V: The ancient Egyptian scribes may have rectly. calculated the 57/20 = 2.850 days period of Algol from long-term observations (1st method). They may not have calculated this 2.850 days period, because the 19 days and 4.7 Two legends 57 days cycles already perfectly predicted all night-time eclipses of Algol (2nd method), or they may have just Lists 1 and 2 are given in Appendix C and D, respectively. These lists are full of extracts from two well known leg- S. Porceddu et al., Algol as Horus in the Cairo Calendar 249 ends: “the Destruction of mankind” (hereafter LE1) and are ordered for “Horus” and “Seth” to determine who “the Contendings of Horus and Seth” (hereafter LE2). is the able and rightful ruler of Egypt, “Horus” being CC texts seem to refer to many lesser known legends as described as physically weak but clever, “Seth” stronger well, but most of the extracts on these lists, chosen by the but with limited intelligence. “Seth” is defeated and two occurrence of the selected SW, are clearly connected to parallel judgements conclude the myth. The first verdict these two well known legends (for example "peace between of the gods is a division of the kingdom between the two, Horus and Seth", "pacify the Wedjat"). Those without a but the second verdict is gods giving “Horus” the entire clear connection to either of these two such as "Horus inheritance of his father “Osiris” (Redford 2001, p294- hears your words in front of every god" or "Horus is pro- 295). Due to parallel judgements, the legend ends either ceeding while Deshret sees his image" could fit into other to the crowning of both “Horus” and “Seth”, or only of narratives. However, these are of generic or fragmentary “Horus”. nature and the associations would be too speculative to Argument VII: Even a quick glance on List 1 (ΘAlgol help to understand the significant periodicity in the prog- order) and List 2 (ΘMoon order) reveals that numerous noses. It is not our ambition here to explain the prognosis CC texts are excerpts from the LE1 and LE2 legends. of all individual dates but to find the logic behind the pe- riodicity, caused by a larger group of connected dates and prognoses. 4.8 Astronomical beliefs behind Lucky and Unlucky Days

4.7.1 Destruction of Mankind (LE1): The scribes used the LE1 and LE2 legends to describe the phases of Algol and the Moon. Here, we show how In this legend, Re sends the Eye of“Horus” (i.e.“Wedjat”) the events of LE1 and LE2 appear in Lists 1 or 2. This to punish the rebellious mankind. reveals the three principles that they possibly used to The legend of the “Destruction of Mankind” is a describe celestial variability as activity of deities. mythological narrative that figures repetitively in CC. It The periods PAlgol and PMoon were discovered from concerns the Eye of “Horus”, also called “Wedjat” or over 500 time points of lucky prognoses (Jetsu et al. N “The Raging One” (Leitz and Budde 2003, p361), fight- 2013). These large samples were used to determine the ing against the rebels who oppose the Sun god “Re”. In zero epochs t0 of ephemerides Eq. 5 and 6. The phase the beginning of this legend, Re sends auxiliary gods in angles of lucky prognoses concentrated at these epochs o o the form of fishes to overhear the plots of the rebellious ΘAlgol = 0 at Aa in Figure 1 and ΘMoon = 0 at Ma mankind (Guilhou 2003). The impudence of mankind in Figure 3. This means that these two particular phase causes “Re” to send the Eye of “Horus” to kill all the angles were considered to be the luckiest in the cycle of rebels. As the Eye takes the form of the lion-goddess Algol and the Moon, respectively. “Sakhmet”, the destruction of the entire mankind is immi- When the CC passages are read in temporal order nent. The gods deceive the goddess “Sakhmet” by colour- from one day to the next, the general sequence of events ing beer mash with hematite to make it look like human appears disorganized. However, the contents of the pas- blood. “Sakhmet” drinks the beer mash, is pacified and sages begin to make sense when these passages are re- mankind is saved (Lichtheim 1976, p197-199). arranged and read in the order of increasing ΘAlgol and ΘMoon (Lists 1 and 2). This result could have been ac- complished even without solving the zero epochs t0 of 4.7.2 Contendings of Horus and Seth (LE2): Eqs. 5 and 6, because the same stories are repeated in the same phase angle order of Algol and the Moon. In In this legend, Horus and Seth contend for the kingship other words, the ΘAlgol and ΘMoon order of these CC of Egypt. passages is unambiguous. Another explicitly quoted legend in CC is the “Con- The first principle in assigning Lucky and Unlucky tendings of Horus and Seth”. After being murdered, the Days seems to have been divine ruler “Osiris” is in the underworld and the con- principle I: The middle of the bright phases of Algol tenders for his office are his son “Horus” and his brother and the Moon is lucky for mankind. “Seth”, who was responsible for the death of “Osiris”. The dispute is decided by the council of nine gods called the For PAlgol, point Aa denotes the luckiest phase angle o “Ennead”, ruled by the Sun god “Re”. Various contests ΘAlgol = 0 in Figure 1. Out of all 28 SWs studied by 250 S. Porceddu et al., Algol as Horus in the Cairo Calendar

Jetsu and Porceddu (2015), the n = 14 lucky time points There are only three lucky time points that mention g(D,M) of “Horus” have the strongest amplifying impact both “Horus” and “Seth” during the same day (Figure 3: on the PAlgol signal (Figure 1: closed squares). Twelve of dark squares and open triangles. Note that the “Horus” o o o these fourteen values, having −90 < PAlgol < +90 , and “Seth” texts at ΘMoon = 73 in List 2 are from two amplify this signal. The closer the phase angle ΘAlgol of different days). The excerpts of these three days are o any g(D,M) is to ΘAlgol =0 , the more this time point o o g(27, 1) ≡ ΘAlgol = 19 ,ΘMoon = 278 , “Peace be- amplifies the P signal. Here are short excerpts from Algol tween Horus and Seth” o the five lucky “Horus” passages closest to ΘAlgol =0 o o g(27, 3) ≡ ΘAlgol = 38 ,ΘMoon = 287 , “Judgement o g(14, 2) ≡ ΘAlgol =6 , “the majesty of Horus receiving between Horus and Seth. Stopping the fight” o o the white crown” g(29, 3) ≡ ΘAlgol = 291 ,ΘMoon = 312 , “ The white o g(19, 12) ≡ ΘAlgol = 13 , “this eye of Horus has come, crown is given to Horus and the red one to is complete, is uninjured” Seth” g(27, 1) ≡ Θ = 19o, “Peace between Horus and Algol In all these three cases, Algol is also at its brightest and Seth” the Moon is waxing gibbous, since half moon had oc- o g(24, 3) ≡ ΘAlgol = 19 , “Onnophris’ happiness in giv- o curred at phase angle Md ≡ ΘMoon = 270 . These texts ing his throne to his son Horus” suggest the reconciliation of the two gods, “Horus” and g(1, 7) ≡ Θ = 32o, “ a feast of entering into Algol “Seth”, thus peace in Egypt and lucky days, when Algol heaven (i.e. appearing into the sky). The two and Moon were simultaneously bright. The White Crown banks of Horus rejoice” (Hedjet) represented the kingship of Upper Egypt and These texts suggest that the lucky prognoses of “Horus” the Red Crown (Deshret) the rulership of Lower Egypt were connected to the bright phases of Algol (Jetsu and (Goebs 2001, p321-325). Porceddu 2015). We know from an unrelated text from Edfu that o For PMoon, the luckiest phase angle ΘMoon =0 co- “Horus” would benefit from the brightening of the Moon: incides with point Ma in Figure 3. Leitz (1994, p285- “When he completes the half month, he assumes control 286,474) had already argued that the New Moon occurred of the sky rejuvenated” (Kaper 2001, p480-482). The CC between the unlucky time points on the first of the fol- text lowing two consecutive days o s(26, 2) ≡ ΘMoon = 270 , “Do not lay the foundation o s(16, 7) ≡ ΘMoon = 173 , “Opening of the windows of a house. Do not stock a workshop. Do not and opening of the court. Seeing the portal of order any job. Do not do any work on this day. the “western side of Thebes”Nwhere his place It is day of opening and closing the court and is. Do not look at the darkness on this day.” the windows of Busiris.” o s(17, 7) ≡ ΘMoon = 185 , (Figure 4: “Seth”) “Do not o coincides with Md ≡ ΘMoon = 270 , the first-quarter speak the name of Seth on this day. Who in moon. his lack of knowledge pronounces his name, he At the moment of Full Moon, “Horus” was declared will not stop fighting in his house of eternity.” “true of voice” and “joyful”; related to his victory over According to his calculations s(16, 7) was the New Moon “Seth” in the divine tribunal (Kaper 2001, p480-482). The day when one is forbidden to go outside and see the unlucky prognoses of “Seth” also show a connection to darkness. The above two unlucky dates are indeed at PMoon, especially to the darker phases of Moon (Figure o both sides of point Mc ≡ ΘMoon = 180 , and exactly 4: open triangles). half a lunar cycle away from the luckiest phase at Ma. The only lucky time point of “Horus” overlapping the This result for the phase angle of the New Moon, Mc thick curved line in Figure 1 (Algol’s primary eclipse), o ≡ ΘMoon = 180 , suggests that the epoch t0 of our mentions ephemeris of Eq. 6 is correct. Hence, the Full Moon is o g(28, 3) ≡ ΘMoon = 164 , “The gods are in jubilation at Ma ≡ Θ =0o. Moon and in joy over the making of will for Horus” The lucky time points g(D,M) having phase angles o it refers to the will made by “Osiris” that raises “Horus” ΘMoon close to ΘMoon = 0 amplify the PMoon sig- nal. The lucky points of “Earth” and “Heaven” have to be the ruler of Egypt. Because of this we can not say that the dark phase of Algol would be always unlucky. the strongest impact on the PMoon signal (Jetsu and Porceddu 2015, p16). However, unlucky days follow immediately after Algol’s S. Porceddu et al., Algol as Horus in the Cairo Calendar 251

o eclipse because the regular distribution of unlucky time s(11, 11) ≡ ΘAlgol = 253 (Figure 2: “Horus”) “the eye points s(D,M) of “Horus”, “Wedjat” and “Sakhmet” con- of Horus raging in front of Re” (LE1) o o centrates at ΘAlgol = 270 (Figure 2). s(10, 6) ≡ ΘAlgol = 259 (Figure 2: “Wedjat”) “coming The “second principle in assigning Lucky and Un- forth of Wedjat” (LE1) o lucky Days” probably was s(27, 8) ≡ ΘAlgol = 265 (Figure 2: “Sakhmet”) “majesty of Sakhmet violates” (LE1) principle II: Use elements from LE1 and LE2 g(16, 4) ≡ Θ = 278o (Figure 1: “Sakhmet”) “day to indirectly describe Algol’s changes (List 1). Algol of the feast of Sakhmet and Bastet” (NC) List 1 contains the translated full CC passages men- o s(13, 6) ≡ ΘAlgol = 278 (Figure 2: “Sakhmet”) “ar- tioning “Horus”, “Wedjat” and “Sakhmet”. The short rival of Sakhmet ... “slaughterer-demons”... excerpts below give a compact presentation of these pas- loose” (NC) sages. We indicate the cases with a clear connection to o s(7, 10) ≡ ΘAlgol = 278 (Figure 2: “Sakhmet”) LE1 or LE2. Our notation “NC” means that there is no ““slaughterer-demons”N of Sakhmet” (NC) clear connection specifically to either myth. o g(23, 7) ≡ ΘAlgol = 291 (Figure 1: “Horus”) “Feast of o g(14, 2) ≡ ΘAlgol = 6 (Figure 1: “Horus”) “Horus Horus in Athribis” (NC) o receiving the white crown” (LE2) g(29, 3) ≡ ΘAlgol = 291 (Figure 1: “Horus”) “white o s(5, 8) ≡ ΘAlgol = 6 (Figure 2: “Horus”) “Horus is crown is given to Horus ... red one to Seth” proceeding while Deshret sees his image” (NC) (LE2) o ≡ o g(1, 5) ≡ ΘAlgol = 13 (Figure 1: “Wedjat”, s(20, 9) ΘAlgol = 291 (Figure 2: “Horus”) “angered “Sakhmet”) “Re ... Sakhmet, ... pacify the on the island ... inspected by ... Horus.” (NC) o Wedjat” (LE1) g(9, 5) ≡ ΘAlgol = 303 (Figure 1: “Sakhmet”) “gods o g(19, 12) ≡ ΘAlgol = 13 (Figure 1: “Horus”) “This eye are joyful over the matter of Sakhmet” (LE1) o of Horus has come, is complete, is uninjured” g(30, 10) ≡ ΘAlgol = 303 (Figure 1: “Wedjat”) “coming (LE1) forth of Shu to bring back Wedjat” (LE1) o ≡ o g(27, 1) ≡ ΘAlgol = 19 (Figure 1: “Horus”) “Peace g(29, 5) ΘAlgol = 309 (Figure 1: “Sakhmet”) “sole between Horus and Seth” (LE2) mistress Sakhmet the great ... gods are pleased” o g(24, 3) ≡ ΘAlgol = 19 (Figure 1: “Horus”) “giving (NC) o his throne to his son Horus” (LE2) g(18, 1) ≡ ΘAlgol = 322 (Figure 1: “Horus”) “mag- o g(1, 7) ≡ ΘAlgol = 32 (Figure 1: “Horus”) “entering nifying the majesty of Horus over his brother” into heaven. The two banks of Horus rejoice” (LE2) o (NC) g(6, 9) ≡ ΘAlgol = 322 (Figure 1: “Wedjat”) “they o g(27, 3) ≡ ΘAlgol = 38 (Figure 1: “Horus”) “Judge- catch Wedjat together with their followers” ment between Horus and Seth. Stopping the (LE1) fight” (LE2) The lucky prognoses of the days related to the main o g(15, 11) ≡ ΘAlgol = 38 (Figure 1: “Horus”) “Horus protagonists of LE1, “Horus”, “Wedjat” and “Sakhmet”, hears your words in front of every god” (NC) had a strong impact on the PAlgol signal (Jetsu and o g(1, 9) ≡ ΘAlgol = 51 (Figure 1: “Horus”) “Feast of Porceddu 2015, p8). All time points of these three deities Horus, the son of Isis” (NC) have extremely similar ΘAlgol distributions (Figures 1 and g(3, 2) ≡ Θ = 57o (Figure 1: “Wedjat”) “Re ... o Algol 2). The lucky prognoses are centered at Aa at ΘAlgol =0 gave the inscription of pacification of Wedjat- in the middle of the brightest phase of Algol (Figure 1). eye” (LE1) The unlucky prognoses of these three SWs concentrate g(7, 9) ≡ Θ = 88o (Figure 1: “Horus”) “followers o Algol close to Ad at ΘAlgol = 270 , immediately after Algol’s of Horus ... in the foreign land” (LE1 or LE2) eclipse (Figure 2). g(28, 3) ≡ Θ = 164o (Figure 1: “Horus”) “the o o Algol The passages between ΘAlgol = 6 and 51 describe making of will for Horus” (LE1 or LE2) feasts or peaceful actions by “Horus”, “Wedjat” and o g(1, 10) ≡ ΘAlgol = 240 (Figure 1: “Horus”) “Horus... “Sakhmet”. Those regarding the crowning or judgement Osiris... Chentechtai... Land” (NC) of “Horus” are related to LE2. The bringing back of o s(26, 1) ≡ ΘAlgol = 253 (Figure 2: “Horus”) “day of “Wedjat” is related to LE1, as well as the pacifications fighting between Horus and Seth” (LE2) of “Sakhmet” or “Wedjat”. The only exception is “Horus o is proceeding while Deshret sees his image” at ΘAlgol =6 252 S. Porceddu et al., Algol as Horus in the Cairo Calendar

o which might not be directly related to either LE1 or LE2. s(12, 2) ≡ ΘMoon = 100 (Figure 4: “Seth”) “His head, Notably, this unlucky date close to point Aa is the only who did rebel against his lord, is cut off” o unlucky time point that deviates from the other seven s(13, 3) ≡ ΘMoon = 117 (Figure 4: “Seth” and unlucky time points concentrated close to Ad in Figure “Osiris”) “day of severing” o 2. s(14, 3) ≡ ΘMoon = 129 (Figure 4: “Osiris”) “gods o The text at ΘAlgol = 57 refers to the order that “Re” are sad over the action against Osiris’ place” o gave in LE1 to save mankind from the wrath of “Wedjat” s(11, 12) ≡ ΘMoon = 137 (Figure 4: “Seth”) “repelled (Eye of“Horus”), synonymous with“Sakhmet”. As Algol’s the confederacy of Seth to the eastern desert” o o eclipse is approaching at ΘAlgol = 88 , “Horus” enters s(14, 5) ≡ ΘMoon = 139 (Figure 4: “Osiris”) “Weep- “the foreign land” (LE1 or LE2). His “will is written” at ing of Isis and Nephthys” o o ΘAlgol = 164 (LE1 or LE2). This particular time point s(18, 3) ≡ ΘMoon = 178 (Figure 4: “Seth”) “tumult by g(28, 3) coincides with the moment when Algol’s eclipse the children of Geb: Seth and his sister Neph- can be observed with naked eye (Figure 1: thick curved thys”’ o line at Ac). s(17, 7) ≡ ΘMoon = 185 (Figure 4: “Seth”) “Do not o The interval between ΘAlgol = 253 and ΘAlgol = speak the name of Seth on this day” o o 291 is filled with descriptions of anger and aggression s(17, 8) ≡ ΘMoon = 190 (Figure 4:“Seth”) “The going by “Horus”, “Wedjat” and “Sakhmet”, or contains hostile of Seth, ... they repelled his followers” o elements such as the “slaughterer-demons”. These spe- s(19, 4) ≡ ΘMoon = 195 (Figure 4: “Osiris”) “Making cific demons were believed to punish mankind on behalf of ointment for Osiris” o of “Sakhmet” and were considered the cause of diseases s(20, 2) ≡ ΘMoon = 197 (Figure 4: “Seth”) “The and symptoms whose pathology was not well understood rebels against their lord were overthrown” o (Lucarelli 2010). Some texts are clearly related to the s(26, 1) ≡ ΘMoon = 266 (Figure 4: “Horus” and transformation of “Wedjat” into the raging “Sakhmet” “Seth”) “day of fighting between Horus and o (LE1). Two out of the three prognoses at ΘAlgol = 291 , Seth” o are lucky. After these three, all remaining texts are lucky, s(24, 8) ≡ ΘMoon = 275 (Figure 4: “Seth”) “Do not i.e. there are only good prognoses in the end of Algol’s pronounce the name of Seth” cycle. This suggests the pacification of “Sakhmet”, as in o Seth’s rebellion is first referred to at ΘMoon = 100 . LE1. “ The coming forth of Shu to bring back Wedjat” It is followed by a long story of “the day of severing” is mentioned at Θ = 303o (LE1). “Shu” succeeds in Algol on s(13, 3). On the next day s(14, 3), “gods are sad over his intention, “ they catch Wedjat together with their fol- the action against Osiris’s place”. “Seth” is repelled in a lowers”, at Θ = 322o (LE1). Then, the same stories Algol tumult (Θ = 137o). The goddesses Isis and Neph- o Moon begin anew at ΘAlgol =6 . o thys are mourning the death of “Osiris” (ΘMoon = 139 ). In short, all the texts of “Wedjat” and “Sakhmet” that o “Seth” causes another tumult (ΘMoon = 178 ). CC ad- were not discussed earlier (Jetsu and Porceddu 2015), also vises not to pronounce his name at New Moon (ΘMoon = support the idea that principle II was used to assign the o o 185 ). His influence begins to wane (ΘMoon = 190 ). prognoses of CC. The order of List 1 texts connected to o “Making of ointment for Osiris” follows at ΘMoon = 195 . LE1 more or less follows the plot of LE1, but the order of o “Seth” is overthrown and judged (ΘMoon = 197 ). Yet, texts connected to LE2 does not follow the plot of LE2. o “Seth” and “Horus” continue their fight (ΘMoon = 266 ). This is not unexpected, because several events are related In the end, CC advises not to pronounce the name of to “Seth”, who is not connected to the PAlgol signal (Jetsu o “Seth” (ΘMoon = 275 ). All these texts are connected and Porceddu 2015). only to LE2. They mostly follow the plot of LE2 in the The “third principle in assigning Lucky and Unlucky order of ΘMoon, but there are contradictions. For exam- Days” could have been ple, the beginning of the cycle would be the expected o principle III: Use LE2 for indirect description place for the fight at ΘMoon = 266 . of the lunar phases (List 2). “Osiris” is also connected to LE2 in the CC. There- fore, it is logical that the unlucky texts of “Osiris” were The unlucky prognosis texts of “Seth” and “Osiris” connected to P (Jetsu and Porceddu 2015, p18). support this idea. These prognoses are very clearly con- Moon The three previously discussed lucky prognoses on centrated to the dark phases of the Moon (Figure 4: open g(27, 1),g(27, 3) and g(29, 3) mentioning both “Seth” and triangles and closed circles). The descriptions from List 2 “Horus” show a reconciliation (LE2) when Algol was at are S. Porceddu et al., Algol as Horus in the Cairo Calendar 253 its brightest and the Moon was waxing gibbous after Md may have more complicated connections to LE1 and LE2, o (ΘMoon = 270 ). or to other myths. It would not be logical to study the texts of “Seth” We can confirm principle I which connects the lucky in connection with LE1, since he is not one of the protag- prognoses to the moments in the middle of the bright onists in the myth. “Horus” personally plays a part only phases of Algol and the Moon. More tentatively, we in LE2, but his Eye is a protagonist in LE1. Neither the present principles II and III, i.e. a specific connection of lucky, nor unlucky, prognoses of “Horus” were connected the LE1 and LE2 myths to the phases of Algol and the to PMoon (Jetsu and Porceddu 2015, p7), i.e. they were Moon. The hemerological tradition had already existed randomly distributed as a function of ΘMoon (Figures 3 for centuries, if not millennia, and accordingly had accu- and 4: closed squares). mulated into itself cultural layers from different historical Because “Horus” is present as a name in both LE1 eras. However, this uncertainty in principles does not al- and LE2, the same texts mentioning “Horus” are repeated ter our main result that the scribes connected the texts when arranged in the order of increasing ΘAlgol (List 1) of the two legends LE1 and LE2 to the phases of Algol and when arranged in the order of increasing ΘMoon (List and the Moon. 2). This means that we have (or the scribes had) a choice Argument VIII: The texts of List 1 (ΘAlgol order) to interpret those texts either in relation to the cycle of and List 2 (ΘMoon order) show that the LE1 and LE2 Algol or the cycle of the Moon. We do not know if the legends could have been used to describe indirectly the scribes faithfully repeated always the same mythological regular changes of Algol and the Moon. texts in relation to the cycle of Algol, the cycle of the Moon or both of these cycles. However, if they did, these “Horus” texts may have a double relation. 4.9 Rejuvenation and kingship The 1st example of a double relation to both Algol and Moon, or to LE1 and LE2, is the text Rejuvenation, the power to disappear and reappear, was associated with “Horus”. g(28, 3) “The gods are in jubilation and in joy over Everything in the ancient Egyptian worldview was the making of will for Horus, son of Osiris, repeating in a cyclic manner: the sky, the celestial phe- to pacify Onnophris in the underworld.” nomena, the Nile, the winds, the clouds, the migrating o At ΘAlgol = 164 , it can describe the return of the lost birds and fish, all life in its individual or holistic sense Eye of Horus during the eclipse of Algol (LE1), but more (Leitz 1994, p452-459). Even the highest power in Egypt, likely it refers to the will made by “Osiris” that raises the divine king, was subject to a continuous cycle, first o “Horus” to be the ruler of Egypt at ΘMoon = 300 (LE2). representing “Horus” on Earth and then “Osiris” in af- It is also related to the time of gestation and infancy terlife. The ancient Egyptian deities were subject to the of “Horus”, when he was hidden from enemies’ sight by same eternal rules of recurrence. his mother Isis. All of these three alternative interpre- The discovery of Algol’s variability might have first tations symbolize the cyclic rejuvenation of royal power astonished the scribes. Had the cause of variability been over Egypt. non-repeating, such as supernova, they would have been The 2nd example is the text baffled by it, but it must have been reaffirming to them to g(7, 9) “The crew and followers of Horus have assem- notice the regularity of Algol’s variability, well suited to bled in the foreign land, to make known that their worldview: the idea of the continuous struggle be- Horus smites him who rebels against his lord.” tween the forces of chaos and order (Magli 2013, p2). It must have taken some effort to incorporate this new phe- On this day, the phase angles of Algol and the Moon nomenon into their religion and mythology, but evidently are nearly equal Θ = 88o and Θ = 73o. The Algol Moon they were able to do that. smiting of the rebels is equally applicable to punishing It was probably of utmost importance to the scribes the mankind for its wicked ways (LE1) and to the battle to determine the period of this phenomenon, because this against “Seth” with his followers (LE2). would have allowed them to interpret correctly the divine However, only the unlucky texts of “Seth” and events relating to it and also to incorporate these events “Osiris” clearly follow the principle III, and perhaps the into their explanation of cosmos. three lucky texts mentioning both “Horus” and “Seth”. We must remember that the ancient Egyptians did Many of the remaining “Horus”, “Seth” or “Osiris” texts not practice natural sciences in the modern sense, but expressed their worldview and all observable phenomena 254 S. Porceddu et al., Algol as Horus in the Cairo Calendar

in the context of religion and myths (von Lieven 2000, 4.10 Astrophysical evidence p188). Many of their discoveries were known only by the experts of religion and magic, the scribes, who could in- The period of Algol must have been shorter three millen- terpret the indirect mythological descriptions of the ob- nia ago (Kwee 1958; Biermann and Hall 1973; Soderhjelm served phenomena. The intention of the writers of CC was 1975). not necessarily to prevent outsiders from understanding It is a fascinating idea that the ancient Egyptians the connections to Algol and the Moon, but for three mil- would have discovered Algol’s variability over three thou- lennia their indirect mythological references have hidden sand years ago, noticed its regularity, determined its from sight the basic periodic principles of assigning Lucky period and incorporated this phenomenon into their and Unlucky Days (i.e. principles I, II and III). mythology. Our modern interpretations of their concepts The idea of rejuvenation was important in ancient are mostly circumstantial. The interpretation of ancient Egyptian mythology. The Moon was used as a symbol Egyptian texts is complex when the phenomena are not of rejuvenation, called “the one that repeats its form” everyday concrete matters such as agriculture, climate, (Kaper 2001, p480-482). Likewise, a vanishing and reap- weather, time keeping, geography or geometry. Although pearing star would have been suggestive of the restoration the CC deals with astronomy only indirectly, it contains of the eye of “Horus” alongside his kingship (Allen 2005, evidence that the scribes made recordings of a concrete p6), (Edwards 1995, p233-240) and (Troy 1989, p132- phenomenon later discovered by modern natural science: 133), and reaffirming of the Egyptians’ cyclic worldview. the regular changes of the eclipsing binary Algol. Sev- The eyes of “Horus” were associated with the crowns of eral astronomical and astrophysical considerations (Jetsu the kings, as symbols of sovereignty (Griffiths 2001, p476- et al. 2013; Jetsu and Porceddu 2015) support the idea 480). Hence, a regularly variable star would naturally be that their prolonged naked eye observations revealed the linked with the divine cycles (“Horus” and his eye), much same discoveries of Algol that Montanari (variability) and like the Moon was seen to have rejuvenative power (Kaper Goodricke (regular variability) made about three millen- 2001, p480-482). Algol’s eclipses could have been consid- nia later. ered the blinding of the eye of “Horus” by “Seth”, but on Naked eye can discover regular variability in the the other hand the return of the Eye of “Horus” would Sun, the Moon, the planets and the variable stars. Jetsu have reaffirmed the restorative, life-giving powers of the et al. (2013) formulated eight astronomical criteria which gods and kings of Egypt. “Horus” or his eye are supposed showed that only the periods of the Moon and Algol could to have been linked with varying celestial objects depend- be discovered from CC, and it was exactly these two pe- ing on the context. Krauss (2016, p137-139) interpreted riods that they rediscovered. Their period analysis also the Eye of Horus in CC to be Venus because the narration showed that 2.850 days is the strongest real periodicity regarding it can also be taken to mean the yearly absence governing the assignment of the lucky prognoses in CC, of Venus from the night sky as it is transformed from a after the lucky prognoses connected to the synodic lunar morning star into an evening star. The dramatic changes month are removed. The mass transfer from Algol B to in the brilliancy of Venus would have been indicative of Algol A is a well established phenomenon (Soderhjelm divine fighting, injuring and rivalry. Additionally, Krauss 1975; Sarna 1993). This mass transfer should cause a pe- suggests that the stars called sehed in the Pyramid Texts riod increase (Kwee 1958; Biermann and Hall 1973). Yet, such as Horus are planets because the text attributes to no-one had confirmed the presence of this phenomenon them the ability to move freely but could this also in- in over 230 years, since Goodricke determined the pe- clude the ability to vanish from the sky? It is logical that riod of Algol in 1783. The period of 2.850 days in CC is Algol would have been represented in mythological texts 0.017 days shorter than the current orbital period of Al- as “Horus” or his eye, as were most of the planets in the gol, 2.867 days. The mass transfer between Algol B and known Egyptian astronomical texts (Clagett 1995, p114). A could have caused this period increase during the past Considering the significance of the name “Horus” to the three millennia. The required mass transfer rate (Jetsu periodic signal, the ancient Egyptians could have believed et al. 2013, p8) was in excellent agreement with the pre- in some connection between Algol, royal power and the dictions of the best evolutionary model of Algol (Sarna cosmic order. 1993, p540). Furthermore, it was shown that Algol’s in- Argument IX: Algol could have been naturally asso- clination has remained stable (Zavala et al. 2010; Baron ciated with “Horus” and called as such, because Algol can et al. 2012), i.e. eclipses occurred also in that historical disappear and reappear. era and the ancient Egyptians would have been able to record these events (Jetsu et al. 2013). S. Porceddu et al., Algol as Horus in the Cairo Calendar 255

Argument X: Astrophysical considerations support of the akhet’ (Coffin Texts 255), are applicable to all but the idea that the 2.850 days period in CC can be the circumpolar stars. Krauss analyzed other passages as well period of Algol. from Coffin Texts and the Book of the Dead which prove the association of the Eye of Horus to something else than the Sun or the Moon. It would be worthwhile to also 4.11 Cultural evidence and lack of it study the celestial diagrams of the Late Period which in- clude Greek and Mesopotamian influences, to discover in Our arguments prove that the ancient Egyptians could greater detail the connection of the Greek constellation have recorded Algol’s period into CC, but the very same of Perseus to the ancient Egyptian star names. arguments do not definitively prove that they did so. How- ever, such cultural aspects are not important for all of our arguments. We will first discuss the arguments that pose 5 Conclusions no problems, and then those that do. There is cultural evidence about the “hour-watchers”, We have presented ten arguments which show that the as well as about the connection between their observa- ancient Egyptian scribes, the “hour-watchers”, had the tions and the religious rituals (Arguments I and II). Al- possible means and the motives for recording the period gol’s variability could have been easily observed in any of Algol in CC. Those arguments are combined here. ancient culture, unless the geographical location of this culture prevented observations (Argument III). Many ex- Argument I: For thousands of years, the “hour- cerpts in List 1 and List 2 are definitively connected to the watchers” practiced the tradition of timekeeping by LE1 and LE2 legends (Argument VII). The order of these observing hour-stars. If Algol was not an hour-star, excerpts in our Lists 1 and 2 is based on statistical analy- it certainly belonged to some hour-star pattern or sis, not on cultural aspects. It is therefore not accidental related constellation. that this order makes sense (Argument VIII). Statisti- The scribes observed regularly about 70 bright stars, or cal, astronomical and astrophysical evidence (Porceddu most probably a lot more, in a region where there are et al. 2008; Jetsu et al. 2013; Jetsu and Porceddu 2015) about 300 clear nights every year. They practiced this supports our last argument (Argument X). tradition for the timing of religious rituals. If the “hour-watchers” noticed Algol’s variability and just recorded the observed eclipses into CC, then modern Argument II: Proper timing of the nightly religious period analysis would detect the 2.850 days periodicity rituals relied on the fixed hour-star patterns. (Arguments IV and V). If the references to Algol and The “hour-watchers” probably discovered Algol’s vari- the Moon in CC are indeed indirect, it is, and it will be, ability from the changes that its eclipses caused in its very difficult to find any definitive cultural proof about hour-star pattern. Argument VI. Statistical analysis by Jetsu and Porceddu Argument III: A naked eye can easily discover the (2015) has revealed a connection between the 2.850 days significant hour-star pattern change caused by Al- period and “Horus”, but our cultural interpretation can gol’s eclipse. be questioned (Argument IX). We do admit that a specific identification of Algol is These changes followed the regular “3+3+16=19” and missing (FAQ 7) but this is a general problem regarding “19+19+19=57” days cycles. all but a few stars and planets. The Pyramid Texts make Argument IV: The scribes could have discovered it obvious that Horus is a star, but the identification of Algol’s 2.850 = 57/20 days period from long-term the star is a matter of debate. Late Period texts iden- observations of the regular 19 and 57 days eclipse tify Horus-son-of-Isis as god of the morning (mentioned cycles. as a star also in Coffin Texts from a much older period, Three alternative methods could have been used in the First Intermediate Period), from which Krauss (2016, recording the 2.850 days period. p137-141) concluded that Horus-son-of-Isis and Haroeris (the elder Horus) are Venus as morning star and evening Argument V: The ancient Egyptian scribes may star. This does not exclude other interpretations, partic- have calculated the 57/20 = 2.850 days period of ularly since we know that many other celestial objects Algol from long-term observations (1st method). received the title or association to Horus. Descriptions They may not have calculated this 2.850 days pe- such as ‘Horus who ascends as gold from upon the lips riod, because the 19 days and 57 days cycles already 256 S. Porceddu et al., Algol as Horus in the Cairo Calendar

perfectly predicted all night-time eclipses of Algol Acknowledgment: We dedicate this paper to the mem- (2nd method), or they may have just recorded the ory of our two co-authors and friends, PhD Jaana Toivari- observed night-time eclipses into CC (3rd method). Viitala (May 16th, 1964 - May 12th, 2017) and prof. Tapio Markkanen (Jan 27th, 1942 - Aug 28th, 2017). We ac- The scribes did not describe Algol’s regular changes di- knowledge PhD Patricia Berg, Dr. Robert J. Demaree, rectly. PhD Heidi Jauhiainen, prof. Karri Muinonen and prof. Argument VI: To avoid violating cosmic order, the Heikki Oja for their comments of the text of this article. scribes would have referred to Algol’s changes only indirectly. Two legends, “the Destruction of Mankind” and “the References Contendings of Horus and Seth”, could have been used to indirectly describe the changes of Algol and Moon. Allen, J. P. 2005, The Ancient Egyptian Pyramid Texts, P. Der Argument VII: Even a quick glance on List 1 Manuelian (Ed.), Society of Biblical Literature, Leiden, The Netherlands. (Θ order) and List 2 (Θ order) reveals Algol Moon Allen, R. H. 1899, Star-names and Their Meanings, that numerous CC texts are excerpts from the LE1 G.E. Stechert, New York, Leipzig [etc.]. and LE2 legends. Assmann, J. and Lorton, D. 2001, The Search for God in Ancient Egypt, Cornell University Press, New York, USA. These two legends were probably used to describe celestial Bacs, T. A. 1990, Two Calendars of Lucky and Unlucky Days, phenomena as activity of gods. Studien zur Altägyptischen Kultur, 17,41–64. Bakir, A. 1966, The Cairo Calendar No. 86637, Government Argument VIII: The texts of List 1 (ΘAlgol order) Printing Office, Cairo, Egypt. and List 2 (Θ order) show that the LE1 and Moon Baron, F., Monnier, J. D., Pedretti, E., Zhao, M., Schaefer, G., LE2 legends could have been used to describe indi- R. Parks, R. et al. 2012, ApJ, 752(1), 20. rectly the regular changes of Algol and the Moon. Belmonte, J. A., Shaltout, M., and Fekri, M. 2009, Astronomy, Landscape and Symbolism: A study of the Orientation of Algol would have been considered as a manifestation of Ancient Egyptian Temples, Supreme Council of Antiquities, “Horus”. ed. J.A. Belmonte and M. Shaltout, Cairo, Egypt. Argument IX: Algol could have been naturally as- Bentley, E. 1986, The Pirandello commentaries. Pirandellian studies. Northwestern University Press, Evanston, Illinois, sociated with “Horus” and called as such, because USA. Algol can disappear and reappear. Biermann, P. and Hall, D. S. 1973, A&A, 27,249–253. We have presented evidence that the period of Algol in Böker, R. 1984, Centaurus, 27,189–217. Brack-Bernsen, L. and Steele, J.M. 2005, Centaurus, 47,181–206. CC was 0.017 days shorter than today (Porceddu et al. Brunner-Traut, E. 1970, Mythos im Alltag. Antaios, 12,332–347 2008; Jetsu et al. 2013; Jetsu and Porceddu 2015). (In German). Argument X: Astrophysical considerations support Clagett, M. 1989, Ancient Egyptian Science 1: Knowledge and Order, American Philosophical Society, Philadelphia, USA. the idea that the 2.850 days period in CC can be Clagett, M. 1995, Ancient Egyptian Science, Vol 2: Calendars, the period of Algol. Clocks and Astronomy, American Philosophical Society, It is not even necessary to present this many arguments Philadephia, USA. Clagett, M. 1999, Ancient Egyptian Science 3: Ancient Egyptian to convince the reader that it would be more compli- Mathematics, American Philosophical Society, Philadephia, cated to explain the statistically significant and accurate USA. 2.850 ± 0.002 days period with something else than Al- Conman, J. 2003, Studien zur Altägyptischen Kultur, 31,33–71. gol. No-one disputes that Algol’s variability is easy to Davis, G. A. 1957, Sky & Telecope, 16,177. observe. The lack of other reasonable alternatives is also Drenkhahn, R. 1972, Zur Anwendung der ’Tagewählkalen- der’, Mitteilungen der Deutschen Archäologischen Instituts, a part of the evidence. It is not only that Algol is the Abteilung Kairo, 28,85–94 (In German). simplest explanation but so far no-one has been able to Edwards, S. 1995, The symbolism of the Eye of Horus in Pyramid think of any other reasonable alternative explanation for Texts, Swansea University, Swansea, UK. the 2.850 days periodicity in CC. If no-one can answer our Goebs, K. 2001, Crowns, D.B. Redford (Ed.), Oxford University last Frequently Asked Question (Appendix B: FAQ 11), Press, New York, USA. then the following famous aphorism by the Italian Nobel Goodricke, J. 1783, a Series of Observations on, and a Discovery of, the Period of the Variation of the Light of the Bright Prize winner Luigi Pirandello must be true: a thing “is Star in the Head of Medusa, Called Algol, In: a Letter from so if it seems so” (Bentley 1986). John Goodricke, Esq. to the Rev. Anthony Shepherd, D. D. S. Porceddu et al., Algol as Horus in the Cairo Calendar 257

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A List of translations to Ancient B Frequently asked questions Egyptian language (FAQ)

We have rewritten innumerable versions of this

ÒfÖ good manuscript. The list below contains some of the most aÀA bad

AÜØ flood season frequently asked questions (FAQ) about our research, as

ÔÖØ winter season well as our short answers. Some of these questions have

ËÑÛ harvest season arisen from misunderstandings of our research. However, aÒÜÝØ snakes we want to answer also those questions, because it was im-

Àb feast possible to foresee them coming, or to prepare answers to gÖÀ night

ÖÛhA evening them beforehand. The sections and the paragraphs (par),

Dd the djed-pillar where our more detailed answers can be found, are given

iÑݹÛÒÛØ hour-watcher in parenthesis. These answers are aimed to ensure that

ØÔØ upper culmination our research better stands the test of time and sceptics.

ËÒ¹dÛAØ heliacal setting The last question 11 is our own. So far, we have not re-

Ñ×ÛØ birth (heliacal rising)

gaÀ ÛÒÑÝ

ÀÖ upon the right shoulder ceived a reasonable alternative answer to this simple ques-

Ñ×DÖ ÛÒÑÝ

ÀÖ upon the right ear tion.

iÖØ ÛÒÑÝ ÀÖ upon the right eye

1. Several CC passages mention different deities, but

aÕA ib

Ö opposite the heart

iÖØ iAbÝ

ÀÖ upon the left eye not all of them are included in your analysis. How

Ñ×DÖ iAbÝ

ÀÖ upon the left ear do you know which one of them determines the cal-

gaÀ iAbÝ ÀÖ upon the left shoulder endar date?

fÒDÛ the snorting one

Answer: The deities do not determine the dates. XÖ ÜÒØÛ the lower Khentu

ØÑÝØ sickness The dates are known (Eqs. 1 and 2, Sect. 2.1: 4th

dÀÖØ bitterness and 6th par, Sect. 2.2: 4th last par).

×ÛÒÛ physician 2. Your statistical analysis is flawed, because the exact ÖÜ healer, wise man historical dating of CC is uncertain.

À×b mathematician Answer: The results of our statistical analysis do ÑAaØ maat, truth, righteousness

ÒËÒÝ raging one not depend on the zero epoch in time. The time

ÜfØعÀÖ¹Òbº× the western side of Thebes points within CC are unambiguously defined and

ÜAØÝÛ slaughterer demons computed (Eqs. 1 and 2). Hence, the results of our ×Àd ÀÑi back turning star statistical analysis would be the same if CC was

AÜ Akh (spirit) dated to ice age, stone age or a million years ahead ÒÀb¹kAÛ Neheb-kau

ÌÑhÛ Tjemehu into the future (Sect. 2.2: 4th last par).

ÒËÑØ Neshmet-bark 3. Your samples are too small to allow reliable statis-

DdfØ reptile tical conclusions.

ÜÖÖ pile of corpses Answer: The ephemerides of Eqs. 5 and 6 are

ÀÛعD×ÖØ Deshret temple building based on large samples of over 500 time points. We use these ephemerides to rearrange the CC passages into the unambiguous order of Lists 1 and 2. These ephemerides work like an accurate modern clock when studying Lists 1 and 2. Furthermore, the bi- nomial significance estimates (Jetsu and Porceddu 2015) QB were reliable even for small samples (Sect. 2.2: 3rd last par). 4. Something must be seriously amiss in your method if a term like "Earth" has a strong correlation with Algol’s period. Answer: The ephemeris of Eq. 5 reveals what the authors of CC wrote when they were observing Al- 260 S. Porceddu et al., Algol as Horus in the Cairo Calendar

gol at its different phases. Nothing is “amiss” in our well the surveys dedicated to astronomical history method, unless those CC texts were not written on and education.” Earth (Sect. 2.2: 3rd last par). This is natural be- 11. If the significant 2.850 days period in CC is not cause feast dates where often described as feasts in connected to Algol, then the following question “Earth” and in “Heaven”. made by Jetsu and Porceddu (2015) needs to be ad- 5. Your CC translations are incomplete. dressed: “What was the origin of the phenomenon Answer: We have used the hieroglyphic transcrip- that occurred every third day, but always 3 hours tion of Leitz (1994) and his original photos of CC, and 36 minutes earlier than before, and caught the as well the translations of Bakir (1966) (in English) attention of Ancient Egyptians?” In other words, and Leitz (1994) (in German). If some translation what happened three times in a row at the night- modifications could be shown to be necessary, this time? Then it occurred during the daytime? After a would not change the general course of events in gap of 13 days, it occurred again during the night- Lists 1 and 2, or the SW identifications (Sect. 2.2: time? 2nd last par). 6. You should establish the statistical validity of your 2 analysis by applying a χ -test to your samples. C List 1 Answer: Unfortunately, this is not possible for our data samples (Sect. 2.2: last par). g(14, 2) ≡ Θ = 6o (Figure 1: “Horus”) “The day 7. A definitive identification of Algol in the Decanal Algol of the majesty of Horus receiving the white or "star clocks" lists is missing. This weakens your crown. His Ennead is in a great celebration. hypotheses. Make offering to the gods of your city. Pacify Answer: It is difficult to identify Egyptian star your “akh”N.” names in general, but such a definitive identification s(5, 8) ≡ Θ = 6o (Figure 2: “Horus”) “The is not needed, because Algol caused easily observ- Algol majesty of Horus is proceeding while Deshret able changes in hour-star patterns or related con- sees his image. Every approach to him is met stellations whether or not it was an actual hour-star with rage.” (Sect. 4.1: 4th-7th par, Sect. 4.2: 5th par). g(1, 5) ≡ Θ = 13o (Figure 1: “Wedjat” and 8. Most of your presented arguments are speculative, Algol “Sakhmet”) and thus your claims are vague and unproven. Your “Doubled are the offerings, presented the rit- presented hypotheses are far from being proved. ual foods. It is the “Neheb-kau”Nfeast of the Answer: This shifts the argumentation from the gods in front of Ptah, in Ta-tenen in all the specific to the general. We make no hypotheses. temples of the gods and goddesses, in front The previous studies have confirmed the presence of Re and his followers. He himself is sur- of the extremely significant 2.850 days period in rounded by Ptah-Sokar, Sakhmet, Nefertem, CC (Jetsu et al. 2013; Jetsu and Porceddu 2015). Horus-Hekenu and Maahes, the son of Bastet. Here, we formulate ten specific Arguments I-X in Light a great fire, pacify the Wedjat. It will be Sects. 4.1- 4.10. It is easy make this type of gen- good on this day.” eral and subjective statements about our research g(19, 12) ≡ Θ = 13o (Figure 1: “Horus”) “Feast for without presenting any evidence against even one Algol your god! Propitiate your “akh”, because this of our ten arguments. eye of Horus has come, is complete, is unin- 9. Your manuscript does not report primary research. jured and there is no claim against it.” Answer: We show that the scribes had the possible g(27, 1) ≡ Θ = 19o (Figure 1: “Horus”) “Peace be- means and motives to write the descriptive texts of Algol tween Horus and Seth. Do not kill any snakes the regular changes of Algol and the Moon into CC. on this day. Make a good day!” This must be primary research, unless someone else g(24, 3) ≡ Θ = 19o (Figure 1: “Horus”) “The ar- has solved this question before us. Algol rival of Isis joyful and Nephthys rejoicing as 10. The scope of your research is unsuitable for this they see Onnophris’ happiness in giving his journal. throne to his son Horus before Re in heaven.” Answer: This journal “disseminates research in g(1, 7) ≡ Θ = 32o (Figure 1: “Horus”) “A day both observational and theoretical astronomy, ... as Algol of feast of Heaven and of Earth, so too of all S. Porceddu et al., Algol as Horus in the Cairo Calendar 261

people. A feast of entering into heaven. The saying he is her brother Seth. Then she called two banks of Horus rejoice.” to this harpoon: Be strong! Be strong! Then o g(27, 3) ≡ ΘAlgol = 38 (Figure 1: “Horus”) “Judge- this Seth shouted to her many times saying: ment between Horus and Seth. Stopping the Do I love the stranger more than the brother fight, hunting the rowers, pacifying the raging of the mother? Then her heart was greatly sad- one. Satisfying of the two lords, causing peace dened and she called to this harpoon: Loosen, to the land. The whole of Egypt is given to Ho- loosen! Behold the brother of the mother. So rus and the whole of desert is given to Seth. was this harpoon driven from him. They stood Coming forth of Thoth who speaks the decree up as two men and each turned his back against in front of Re.” another. Then the majesty of Horus was an- o g(15, 11) ≡ ΘAlgol = 38 (Figure 1: “Horus”) “If you gered against his mother Isis like a panther. see a thing, it is good. Horus hears your words She placed it in front of him.” o in front of every god and every goddess on this s(11, 11) ≡ ΘAlgol = 253 (Figure 2: “Horus”) “Re’s day, concerning every good thing you see in bringing of the great ones to the booth to see your house.” what he had seen through the eye of Horus the o g(1, 9) ≡ ΘAlgol = 51 (Figure 1: “Horus”) “Feast of Elder. Then their faces were turned down see- Horus, the son of Isis. His followers in ...” ing the eye of Horus raging in front of Re. Do o g(3, 2) ≡ ΘAlgol = 57 (Figure 1: “Wedjat”) “The not perform any ritual in any house on this coming forth of Thoth in the presence of Re in day.” o the hidden shrine. He gave the inscription of s(10, 6) ≡ ΘAlgol = 259 (Figure 2: “Wedjat”) “The the pacification of the Wedjat-eye; Hu , Sia and coming forth of Wedjat into the presence of the followers of Maat obey Neith, the crown- the favoured ones in Heliopolis. The promotion goddess in his retinue. If you see anything, it of the Majesty of the shrines through Mnevis- will be good on this day.” bull, the herald of Re, whom Maat raised up to o g(7, 9) ≡ ΘAlgol = 88 (Figure 1: “Horus”) “The crew Atum.” o and followers of Horus have assembled in the s(27, 8) ≡ ΘAlgol = 265 (Figure 2: “Sakhmet”) “Do foreign land, to make known that Horus smites not go out of your house until the setting of the him who rebels against his lord. Every land is sun because the majesty of Sakhmet violates content, their hearts in great joy.” in “Tjemehu”N, where she is walking without o g(28, 3) ≡ ΘAlgol = 164 (Figure 1: “Horus”) “The anyone nearby.” o gods are in jubilation and in joy over the mak- g(16, 4) ≡ ΘAlgol = 278 (Figure 1: “Sakhmet”) “This ing of will for Horus, son of Osiris, to pacify is the day of the feast of Sakhmet and Bastet Onnophris in the underworld. Then the land is in Asheru for Re, given in front of Re.” o in feast and the hearts of the gods are pleased. s(13, 6) ≡ ΘAlgol = 278 (Figure 2: “Sakhmet”) “Do If you see anything, it will be good on this day.” not go out of your house to any road on this o g(1, 10) ≡ ΘAlgol = 240 (Figure 1: “Horus”) “Horus... day. This is the day of the arrival of Sakhmet Osiris... Chentechtai... Land” of Reheset. Their great “slaughterer-demons” o s(26, 1) ≡ ΘAlgol = 253 (Figure 2: “Horus”) “Do not were let loose from Letopolis on this day.” o do anything on this day. This is the day of s(7, 10) ≡ ΘAlgol = 278 (Figure 2: “Sakhmet”) “Do fighting between Horus and Seth. Every man not go out of your house to spend time until the grasped his fellow and they were on their sides setting of the sun to the horizon. This is the as two men. They were turned into two ebonies day of the hidden-named “slaughterer-demons” in the netherworld of the lords of Babylon. of Sakhmet...” o Three days and nights were spent in this man- g(23, 7) ≡ ΘAlgol = 291 (Figure 1: “Horus”) “Feast of ner. Then Isis let their harpoons fall. It fell Horus in Athribis on this day of his years, in in front of her son Horus. Then he called with his great and beautiful images.” o a loud voice saying he is her son Horus. Then g(29, 3) ≡ ΘAlgol = 291 (Figure 1: “Horus”) “Coming Isis called to this harpoon: Loosen, loosen from forth of the three ancestors inside the Tanenet son Horus! Then this harpoon loosened from in front of Ptah, beautiful of face, while ador- her son Horus. Then she let fall another har- ing Re of the throne of the truth of the god- poon in front of her brother Seth. He shouted dess temples. The white crown is given to Ho- 262 S. Porceddu et al., Algol as Horus in the Cairo Calendar

o rus and the red one to Seth. Their hearts are g(9, 4) ≡ ΘMoon = 73 (Figure 3: “Seth”) “It is the pleased upon them.” day of doing what Thoth did. ’The djed-pillars o s(20, 9) ≡ ΘAlgol = 291 (Figure 2: “Horus”) “The endure’, says Re in front of the great ones, judgement of Maat in front of these gods, an- whereupon these gods together with Thoth let gered on the island of the sanctuary of Letopo- the enemy of Seth kill himself in front of lis, inspected by the majesty of Horus.” his sanctuary. This is what was done by the o g(9, 5) ≡ ΘAlgol = 303 (Figure 1: “Sakhmet”) “The “slaughterer-demons” of Qesret on this day.” o gods are joyful over the matter of Sakhmet. g(7, 9) ≡ ΘMoon = 73 (Figure 3: “Horus”) “The crew The day of establishing the food offerings and and followers of Horus have assembled in the reversion-offering, which are pleasing to the foreign land, to make known that Horus smites gods and the “akh”.” him who rebels against his lord. Every land is o g(30, 10) ≡ ΘAlgol = 303 (Figure 1: “Wedjat”) “The content, their hearts in great joy.” o coming forth of Shu to bring back Wedjat, paci- g(11, 4) ≡ ΘMoon = 98 (Figure 3: “Osiris”) “Feast fied by Thoth on this day. House of Re. House of Osiris in Abydos in the great “neshmet- of Osiris. House of Horus.” bark”Non this day. The dead are in jubilation.” o o g(29, 5) ≡ ΘAlgol = 309 (Figure 1: “Sakhmet”) “Ap- s(12, 2) ≡ ΘMoon = 100 (Figure 4: “Seth”) “This is pearance in glory in the sight of Hu by Thoth the day of raising his head by the one who re- to send this decree southwards to instruct the belled against his lord. His intent is destroyed two lands of Bastet together with the sole mis- and the staff of Seth, son of Nut. His head, tress Sakhmet the great. The gods are pleased. who did rebel against his lord, is cut off.” o If you see anything, it will be good on this day.” s(13, 3) ≡ ΘMoon = 117 (Figure 4: “Seth” and o g(18, 1) ≡ ΘAlgol = 322 (Figure 1: “Horus”) “If you “Osiris”) “This is the day of severing... see anything, it will be good on this day. This the ferryman upon the uncrossable river of is the day of magnifying the majesty of Horus snakes... every hall to this “neshmet-bark” of over his brother, which they did at the gate.” Osiris, sailing southwards to Abydos, to the o g(6, 9) ≡ ΘAlgol = 322 (Figure 1: “Wedjat”) “The great city of Onnophris. For he has made his coming of the great ones from the House of Re. form into one old and small in the arms of Joy on this day, as they catch Wedjat together (translation unknown)... given gold as reward with their followers. If you see anything, it will to Nemti for fare, saying ’Ferry us to the west!’ be good on this day.” Then he received it... upon a limb of the di- vine body, whereupon was this association be- hind him as an army of “reptiles”N. Then they D List 2 knew Seth had made these gods enter to purify the limb of the divine body. Then they revived it... he came... the enemy behind him on the g(1, 9) ≡ Θ = 0o (Figure 3: “Horus”) “Feast of Moon water. Then they changed their forms into lit- Horus, the son of Isis. His followers in ...” tle, small cattle. Then these gods made a “pile g(1, 10) ≡ Θ = 5o (Figure 3: “Horus” and Moon of corpses”Nand split them entirely. Then was “Osiris”) “Horus... Osiris... Chentechtai... taken action upon the tongue of the enemy of Land” Nemti. Do not approach the gold in the house s(5, 8) ≡ Θ = 44o (Figure 4: “Horus”) “The Moon of Nemti as far as this day. So began the re- majesty of Horus is proceeding while Deshret moval of the little, small cattle from the west, sees his image. Every approach to him is met so began the creation of the herds of little, with rage.” small cattle as far as this day. ” g(6, 7) ≡ Θ = 51o (Figure 3: “Osiris”) “Joy of Moon g(14, 2) ≡ Θ = 124o (Figure 3: “Horus”) “The Osiris at the tomb of Busiris. The coming forth Moon day of the majesty of Horus receiving the white of Anubis, adoration in his wake, likewise he crown. His Ennead is in a great celebration. has received all people. (his) adorers (or, ado- Make offering to the gods of your city. Pacify ration) following him; he has received every- your akh.” body in the hall. Perform a ritual!” o s(14, 3) ≡ ΘMoon = 129 (Figure 4: “Osiris”) “Do not do anything on this day. The hearts of the gods S. Porceddu et al., Algol as Horus in the Cairo Calendar 263

are sad over the action against Osiris’ place been reckoned on his day. These gods became of embalming and the action of the enemy of aware of him, they repelled his followers and Nemti. All born on this day will die of cuts.” none of them remained.” o o s(11, 11) ≡ ΘMoon = 132 (Figure 4: “Horus”) “Re’s s(19, 4) ≡ ΘMoon = 195 (Figure 4: “Osiris”) “Stealing bringing of the great ones to the booth to see of property inside the Deshret “temple build- what he had seen through the eye of Horus the ing”N. Making of ointment for Osiris in front Elder. Then their faces were turned down see- of the funerary workshop. Do not taste bread ing the eye of Horus raging in front of Re. Do or beer on this day. Drink the juice of grapes not perform any ritual in any house on this until Re sets.” o day.” s(20, 2) ≡ ΘMoon = 197 (Figure 4: “Seth”) “This is o s(11, 12) ≡ ΘMoon = 137 (Figure 4: “Seth”) “The the day of giving food-offerings in front of Re causers of tumult are in front of the follow- and followers by Thoth. The act in there was ers of Re, who repelled the confederacy of Seth done accordingly. The rebels against their lord to the eastern desert.” were overthrown. Then they lifted up Seth, son o s(14, 5) ≡ ΘMoon = 139 (Figure 4: “Osiris”) “Weep- of Nut; so they became lowered by the gods.” o ing of Isis and Nephthys. It is the day of their s(20, 9) ≡ ΘMoon = 231 (Figure 4: “Horus”) “The mourning Osiris in Busiris in remembrance of judgement of Maat in front of these gods, an- that which he had seen. Do not listen to singing gered on the island of the sanctuary of Letopo- or music on this day.” lis, inspected by the majesty of Horus.” o o g(16, 2) ≡ ΘMoon = 149 (Figure 3: “Osiris”) “Feast of g(19, 12) ≡ ΘMoon = 234 (Figure 3: “Horus”) “Feast Osiris-Onnophris. The gods who are in his at- for your god! Propitiate your “akh”, because tendance are in great celebration. The Ennead this eye of Horus has come, is complete, is un- is before Re, joyful. If you see anything on this injured and there is no claim against it.” o day, it will be good. ” g(24, 3) ≡ ΘMoon = 251 (Figure 3: “Horus”) “The o g(13, 12) ≡ ΘMoon = 161 (Figure 3: “Seth” and arrival of Isis joyful and Nephthys rejoicing “Osiris”) “A holiday because of protecting the as they see Onnophris’ happiness in giving his son of Osiris. . . at the back of the portal by throne to his son Horus before Re in heaven.” o Seth.” g(23, 7) ≡ ΘMoon = 258 (Figure 3: “Horus”) “Feast o g(18, 1) ≡ ΘMoon = 168 (Figure 3: “Horus”) “If you of Horus in Athribis on this day of his years, see anything, it will be good on this day. This in his great and beautiful images.” o is the day of magnifying the majesty of Horus s(26, 1) ≡ ΘMoon = 266 (Figure 4: “Horus” and over his brother, which they did at the gate.” “Seth”) “Do not do anything on this day. This o s(18, 3) ≡ ΘMoon = 178 (Figure 4: “Seth”) ”This is is the day of fighting between Horus and Seth. the day of tumult by the children of Geb: Seth Every man grasped his fellow and they were and his sister Nephthys. Do not approach any on their sides as two men. They were turned road until the deed is done on this day.” into two ebonies in the netherworld of the lords o g(15, 11) ≡ ΘMoon = 180 (Figure 3: “Horus”) “If you of Babylon. Three days and nights were spent see a thing, it is good. Horus hears your words in this manner. Then Isis let their harpoons in front of every god and every goddess on this fall. It fell in front of her son Horus. Then day, concerning every good thing you see in he called with a loud voice saying he is her your house.” son Horus. Then Isis called to this harpoon: o g(17, 6) ≡ ΘMoon = 180 (Figure 3: “Osiris”) “This is Loosen, loosen from son Horus! Then this har- the day of bringing to the embalming place of poon loosened from her son Horus. Then she Osiris those offerings which have been placed let fall another harpoon in front of her brother in the hands of Anubis.” Seth. He shouted saying he is her brother Seth. o s(17, 7) ≡ ΘMoon = 185 (Figure 4: “Seth”) “Do not Then she called to this harpoon: Be strong! Be speak the name of Seth on this day. Who in strong! Then this Seth shouted to her many his lack of knowledge pronounces his name, he times saying: Do I love the stranger more than will not stop fighting in his house of eternity.” the brother of the mother? Then her heart was o s(17, 8) ≡ ΘMoon = 190 (Figure 4:“Seth”) “The going greatly saddened and she called to this har- of Seth, son of Nut, to the brawlers that have poon: Loosen, loosen! Behold the brother of the 264 S. Porceddu et al., Algol as Horus in the Cairo Calendar

mother. So was this harpoon driven from him. They stood up as two men and each turned his back against another. Then the majesty of Ho- rus was angered against his mother Isis like a panther. She placed it in front of him.” o s(24, 8) ≡ ΘMoon = 275 (Figure 4: “Seth”) “Do not pronounce the name of Seth. Do not raise your voice on this day. This is the day of Onnophris. As to anyone who pronounces his name in ignorance, he shall not cease fighting in his house for ever.” o g(27, 1) ≡ ΘMoon = 278 (Figure 3: “Horus” and “Seth”) “Peace between Horus and Seth. Do not kill any snakes on this day. Make a good day!” o g(27, 3) ≡ ΘMoon = 287 (Figure 3: “Horus” and “Seth”) “Judgement between Horus and Seth. Stopping the fight, hunting the rowers, pacify- ing the raging one. Satisfying of the two lords, causing peace to the land. The whole of Egypt is given to Horus and the whole of desert is given to Seth. Coming forth of Thoth who speaks the decree in front of Re.” o g(28, 3) ≡ ΘMoon = 300 (Figure 3: “Horus” and “Osiris”) “The gods are in jubilation and in joy over the making of will for Horus, son of Osiris, to pacify Onnophris in the underworld. Then the land is in feast and the hearts of the gods are pleased. If you see anything, it will be good on this day.” o g(29, 3) ≡ ΘMoon = 312 (Figure 3: “Horus” and “Seth”) “Coming forth of the three ancestors inside the Tanenet in front of Ptah, beautiful of face, while adoring Re of the throne of truth of the goddess temples. The white crown is given to Horus and the red one to Seth. Their hearts are pleased upon them.” o g(28, 7) ≡ ΘMoon = 319 (Figure 3: “Osiris”) “Feast of Osiris in Abydos. The majesty of Onnophris raised up the willow.” o g(1, 7) ≡ ΘMoon = 351 (Figure 3: “Horus”) “A day of feast of Heaven and of Earth, so too of all people. A feast of entering into heaven. The two banks of Horus rejoice.”